Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26044254 | C2 | semidirect |
| 2. #26044254 | C2 | semidirect |
| 3. #26044247 | C2 | semidirect |
| 4. #26044245 | C2 | semidirect |
| 5. #26044244 | C2 | semidirect |
| 6. #26044243 | C2 | semidirect |
| 7. #26044240 | C2 | semidirect |
| 8. #26044238 | C2 | semidirect |
| 10. C4×C22⋊D367 | C2 | semidirect |
| 11. (C22⋊D367)⋊C4 | C2 | semidirect |
| 12. #26044220 | C2 | semidirect |
| 13. #26044217 | C2 | semidirect |
| 14. C2×C22⋊Dic367 | C2 | semidirect |
| 15. C2×C22⋊C4×C367 | C2 | semidirect |
| 16. C2×Dic734 | C22 | semidirect |
| 22. C2×C4×D367 | C22 | semidirect |
| 23. C4⋊Dic367 | C22 | semidirect |
| 24. C4⋊Dic367 | C22 | semidirect |
| 25. C4⋊Dic367 | C22 | semidirect |
| 26. Dic367⋊C4 | C22 | semidirect |
| 27. Dic367⋊C4 | C22 | semidirect |
| 28. Dic367⋊C4 | C22 | semidirect |
| 29. Dic367⋊C4 | C22 | semidirect |
| 30. Dic367⋊C4 | C22 | semidirect |
| 38. (C2×D367)⋊C4 | C22 | semidirect |
| 39. (C2×D367)⋊C4 | C22 | semidirect |
| 40. (C2×D367)⋊C4 | C22 | semidirect |
| 41. C4×Dic367 | C22 | semidirect |
| 42. C4×Dic367 | C22 | semidirect |
| 43. C4×Dic367 | C22 | semidirect |
| 110. C367 | #551 | semidirect |
| 126. C2×C22⋊C4 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044254 | 2 |
| #26044247 | 2 |
| #26044245 | 2 |
| #26044244 | 2 |
| #26044243 | 2 |
| #26044240 | 2 |
| #26044238 | 2 |
| #26044230 | 2 |
| C4×C22⋊D367 | 2 |
| (C22⋊D367)⋊C4 | 2 |
| #26044220 | 2 |
| #26044217 | 2 |
| C2×C22⋊Dic367 | 2 |
| C2×C22⋊C4×C367 | 2 |
| #551 | 367 |