Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26041990 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041577 | C2 | semidirect |
| 5. #26041566 | C2 | semidirect |
| 6. #26041473 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 9. #26041388 | C2 | semidirect |
| 10. C4×D1448 | C2 | semidirect |
| 11. #486×C181 | C2 | semidirect |
| 80. D724 | #41 | semidirect |
| 129. C181 | #3366 | semidirect |
| 134. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| #26041949 | 2 |
| #26041642 | 2 |
| #26041577 | 2 |
| #26041566 | 2 |
| #26041473 | 2 |
| #26041471 | 2 |
| #26041409 | 2 |
| #26041388 | 2 |
| C4×D1448 | 2 |
| #486×C181 | 2 |
| #3366 | 181 |