Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #26041933 | C2 | semidirect |
| 2. #26041625 | C2 | semidirect |
| 3. #26041595 | C2 | semidirect |
| 4. #26041564 | C2 | semidirect |
| 5. #26041530 | C2 | semidirect |
| 6. #26041471 | C2 | semidirect |
| 7. #26041424 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041357 | C2 | semidirect |
| 10. #26041280 | C2 | semidirect |
| 11. #550×C181 | C2 | semidirect |
| 92. Q8×C181 | #41 | semidirect |
| 134. C181 | #3332 | semidirect |
| 136. #550 | D181 | semidirect |
| 217. Q8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041625 | 2 |
| #26041595 | 2 |
| #26041564 | 2 |
| #26041530 | 2 |
| #26041471 | 2 |
| #26041424 | 2 |
| C4×#15668436 | 2 |
| #26041357 | 2 |
| #26041280 | 2 |
| #550×C181 | 2 |
| #3332 | 181 |