Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #26042014 | C2 | semidirect |
| 2. #26042002 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041652 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041495 | C2 | semidirect |
| 7. #26041490 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. C4×#15668438 | C2 | semidirect |
| 11. C8×Q8×C181 | C2 | semidirect |
| 125. C181 | #3394 | semidirect |
| 135. C8×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| #26042002 | 2 |
| #26041663 | 2 |
| #26041652 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| #26041490 | 2 |
| #26041475 | 2 |
| C4×#15668438 | 2 |
| C8×Q8×C181 | 2 |
| #3394 | 181 |