Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #26041611 | C2 | semidirect |
| 4. #26041599 | C2 | semidirect |
| 5. #26041566 | C2 | semidirect |
| 6. #26041561 | C2 | semidirect |
| 7. #26041509 | C2 | semidirect |
| 8. C4×#15668438 | C2 | semidirect |
| 9. C8×D724 | C2 | semidirect |
| 10. #106×D181 | C2 | semidirect |
| 11. #498×C181 | C2 | semidirect |
| 81. D724 | SD16 | semidirect |
| 100. C8×C181 | #41 | semidirect |
| 123. C181 | #3335 | semidirect |
| 127. #498 | D181 | semidirect |
| 224. C8 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| #26041932 | 2 |
| #26041611 | 2 |
| #26041599 | 2 |
| #26041566 | 2 |
| #26041561 | 2 |
| #26041509 | 2 |
| C4×#15668438 | 2 |
| C8×D724 | 2 |
| #106×D181 | 2 |
| #498×C181 | 2 |
| #3335 | 181 |