Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26041988 | C2 | semidirect |
| 2. #26041683 | C2 | semidirect |
| 3. #26041681 | C2 | semidirect |
| 4. #26041680 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041579 | C2 | semidirect |
| 7. #26041567 | C2 | semidirect |
| 8. C8×Dic362 | C2 | semidirect |
| 61. D8×C181 | Q8 | semidirect |
| 108. C181 | #3380 | semidirect |
| 154. D8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041988 | 2 |
| #26041683 | 2 |
| #26041681 | 2 |
| #26041680 | 2 |
| #26041581 | 2 |
| #26041579 | 2 |
| #26041567 | 2 |
| C8×Dic362 | 2 |
| D8×Dic181 | 2 |
| C4×D8×C181 | 2 |
| #3380 | 181 |