Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. M16×D367 | C2 | semidirect |
| 3. #26044218 | C2 | semidirect |
| 4. #26044189 | C2 | semidirect |
| 5. #26044188 | C2 | semidirect |
| 6. #26044187 | C2 | semidirect |
| 7. #104×C367 | C2 | semidirect |
| 8. #19154578 | C4 | semidirect |
| 12. #19154576 | C4 | semidirect |
| 13. Q8×D367 | C4 | semidirect |
| 15. D4×D367 | C4 | semidirect |
| 18. #19154561 | C22 | semidirect |
| 23. C4×Dic367 | C22 | semidirect |
| 25. M16×C367 | C22 | semidirect |
| 26. C42×C367 | C22 | semidirect |
| 75. C367 | #421 | semidirect |
| 83. #104 | D367 | semidirect |
| 97. M16 | C2×D367 | semidirect |
| 102. C42 | C2×D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D367 | 2 |
| M16×D367 | 2 |
| #26044218 | 2 |
| #26044189 | 2 |
| #26044188 | 2 |
| #26044187 | 2 |
| #104×C367 | 2 |
| #421 | 367 |