Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #26042002 | C2 | semidirect |
| 2. #26041989 | C2 | semidirect |
| 3. #26041634 | C2 | semidirect |
| 4. #26041630 | C2 | semidirect |
| 5. #26041587 | C2 | semidirect |
| 6. #26041570 | C2 | semidirect |
| 8. #26041485 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 11. C8×Q8×C181 | C2 | semidirect |
| 120. C181 | #3360 | semidirect |
| 130. C8×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041989 | 2 |
| #26041634 | 2 |
| #26041630 | 2 |
| #26041587 | 2 |
| #26041570 | 2 |
| #26041495 | 2 |
| #26041485 | 2 |
| C4×#15668438 | 2 |
| C4×D1448 | 2 |
| C8×Q8×C181 | 2 |
| #3360 | 181 |