Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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. #26042330 | C2 | semidirect |
| 2. #26042329 | C2 | semidirect |
| 3. #26042328 | C2 | semidirect |
| 4. Q8×#13089685 | C2 | semidirect |
| 34. D181⋊C8 | Q8 | semidirect |
| 94. C181 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042330 | 2 |
| #26042329 | 2 |
| #26042328 | 2 |
| Q8×#13089685 | 2 |
| #26042286 | 2 |
| #26042283 | 2 |
| #26042244 | 2 |
| C4×D181⋊C8 | 2 |
| #26041834 | 2 |
| #2960 | 181 |