Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041979 | C2 | semidirect |
| 2. #26041681 | C2 | semidirect |
| 3. #26041601 | C2 | semidirect |
| 4. #26041591 | C2 | semidirect |
| 5. #26041579 | C2 | semidirect |
| 6. #26041529 | C2 | semidirect |
| 7. #26041358 | C2 | semidirect |
| 8. #26041320 | C2 | semidirect |
| 9. C4×D8×C181 | C2 | semidirect |
| 102. C181 | #3355 | semidirect |
| 110. C4×D8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041979 | 2 |
| #26041681 | 2 |
| #26041601 | 2 |
| #26041591 | 2 |
| #26041579 | 2 |
| #26041529 | 2 |
| #26041358 | 2 |
| #26041320 | 2 |
| C4×D8×C181 | 2 |
| #3355 | 181 |