Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041999 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041604 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041525 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041432 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. #26041285 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 15. C2×#15668438 | C22 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 20. #19153795 | C22 | semidirect |
| 24. C4×Dic362 | C22 | semidirect |
| 27. #19153775 | C22 | semidirect |
| 28. #19153750 | C22 | semidirect |
| 29. #19153748 | C22 | semidirect |
| 30. #19153741 | C22 | semidirect |
| 33. #19153738 | C22 | semidirect |
| 34. #19153738 | C22 | semidirect |
| 35. #19153738 | C22 | semidirect |
| 36. C2×M16×C181 | C22 | semidirect |
| 38. C4⋊C8×C181 | C22 | semidirect |
| 39. C22⋊C8×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 135. C181 | #3324 | semidirect |
| 146. #436 | D181 | semidirect |
| 152. C2×M16 | C2×D181 | semidirect |
| 168. C4⋊C8 | C2×D181 | semidirect |
| 175. C22⋊C8 | C2×D181 | semidirect |
| 176. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| D4×D724 | 2 |
| #26041626 | 2 |
| #26041604 | 2 |
| #26041560 | 2 |
| #26041525 | 2 |
| #26041480 | 2 |
| #26041432 | 2 |
| C4×#15668438 | 2 |
| #26041285 | 2 |
| #436×C181 | 2 |
| #3324 | 181 |