Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041986 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041625 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041570 | C2 | semidirect |
| 7. #26041472 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041391 | C2 | semidirect |
| 10. C4×#15668434 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 97. D4×C181 | #41 | semidirect |
| 129. C181 | #3366 | semidirect |
| 138. #459 | D181 | semidirect |
| 218. D4 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| #26041949 | 2 |
| #26041642 | 2 |
| #26041625 | 2 |
| #26041581 | 2 |
| #26041570 | 2 |
| #26041472 | 2 |
| #26041406 | 2 |
| #26041391 | 2 |
| C4×#15668434 | 2 |
| #459×C181 | 2 |
| #3366 | 181 |