Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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. #26041990 | C2 | semidirect |
| 2. #26041986 | C2 | semidirect |
| 3. #26041682 | C2 | semidirect |
| 4. #26041679 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041578 | C2 | semidirect |
| 7. #26041570 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 47. #15668434 | Q8 | semidirect |
| 119. C181 | #3380 | semidirect |
| 128. #476 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041990 | 2 |
| #26041986 | 2 |
| #26041682 | 2 |
| #26041679 | 2 |
| #26041581 | 2 |
| #26041578 | 2 |
| #26041570 | 2 |
| #26041403 | 2 |
| C4×#15668434 | 2 |
| #26041359 | 2 |
| #476×C181 | 2 |
| #3380 | 181 |