Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #26041753 | C2 | semidirect |
| 3. #26041295 | C2 | semidirect |
| 4. #26041285 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041036 | C2 | semidirect |
| 7. #344×C181 | C2 | semidirect |
| 12. C2×#15668438 | C4 | semidirect |
| 13. C2×D1448 | C4 | semidirect |
| 30. C2×Dic362 | C2×C4 | semidirect |
| 35. C2×D724 | C2×C4 | semidirect |
| 56. C2×C8×C181 | C2×C4 | semidirect |
| 115. C181 | #1904 | semidirect |
| 122. #344 | D181 | semidirect |
| 165. C2×C8 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| #26041753 | 2 |
| #26041295 | 2 |
| #26041285 | 2 |
| #26041252 | 2 |
| #26041036 | 2 |
| #344×C181 | 2 |
| #1904 | 181 |