Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042009 | C2 | semidirect |
| 3. #26041686 | C2 | semidirect |
| 4. #26041682 | C2 | semidirect |
| 5. #26041589 | C2 | semidirect |
| 6. #26041575 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 46. #15668437 | Q8 | semidirect |
| 115. C181 | #3385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042009 | 2 |
| #26041986 | 2 |
| #26041686 | 2 |
| #26041682 | 2 |
| #26041589 | 2 |
| #26041575 | 2 |
| #26041557 | 2 |
| #26041406 | 2 |
| #26041376 | 2 |
| C4×#15668437 | 2 |
| #476×C181 | 2 |
| #3385 | 181 |