Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26042303 | C2 | semidirect |
| 2. #26042300 | C2 | semidirect |
| 3. #26042295 | C2 | semidirect |
| 4. #26042283 | C2 | semidirect |
| 5. D181⋊(C4⋊C8) | C2 | semidirect |
| 7. #26042244 | C2 | semidirect |
| 108. C181 | #2925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042303 | 2 |
| #26042300 | 2 |
| #26042295 | 2 |
| #26042283 | 2 |
| D181⋊(C4⋊C8) | 2 |
| #26042253 | 2 |
| #26042244 | 2 |
| C4×#15668448 | 2 |
| #2925 | 181 |