Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 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. #26041989 | C2 | semidirect |
| 3. #26041675 | C2 | semidirect |
| 4. #26041608 | C2 | semidirect |
| 5. #26041599 | C2 | semidirect |
| 6. #26041570 | C2 | semidirect |
| 7. #26041511 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041344 | C2 | semidirect |
| 10. #106×D181 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 80. D724 | SD16 | semidirect |
| 90. #13089678 | #41 | semidirect |
| 123. C181 | #3335 | semidirect |
| 131. #475 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041989 | 2 |
| #26041932 | 2 |
| #26041675 | 2 |
| #26041608 | 2 |
| #26041599 | 2 |
| #26041570 | 2 |
| #26041511 | 2 |
| C4×#15668436 | 2 |
| #26041344 | 2 |
| #106×D181 | 2 |
| #475×C181 | 2 |
| #3335 | 181 |