Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26042008 | C2 | semidirect |
| 3. #26041686 | C2 | semidirect |
| 4. #26041684 | C2 | semidirect |
| 6. #26041572 | C2 | semidirect |
| 7. #26041564 | C2 | semidirect |
| 9. #26041409 | C2 | semidirect |
| 64. SD16×C181 | Q8 | semidirect |
| 85. Q8×C181 | C2×Q8 | semidirect |
| 96. C8×C181 | C2×Q8 | semidirect |
| 116. C181 | #3386 | semidirect |
| 167. SD16 | Dic362 | semidirect |
| 196. Q8 | C2×Dic362 | semidirect |
| 213. C8 | C2×Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| D4×Dic362 | 2 |
| #26041686 | 2 |
| #26041684 | 2 |
| #26041577 | 2 |
| #26041572 | 2 |
| #26041564 | 2 |
| #26041559 | 2 |
| #26041409 | 2 |
| #26041380 | 2 |
| C4×SD16×C181 | 2 |
| #3386 | 181 |