Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041986 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041687 | C2 | semidirect |
| 4. #26041677 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041569 | C2 | semidirect |
| 7. #26041567 | C2 | semidirect |
| 8. #26041559 | C2 | semidirect |
| 9. #26041409 | C2 | semidirect |
| 65. D8×C181 | Q8 | semidirect |
| 89. D4×C181 | C2×Q8 | semidirect |
| 98. C8×C181 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 174. D8 | Dic362 | semidirect |
| 204. D4 | C2×Dic362 | semidirect |
| 220. C8 | C2×Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| D4×Dic362 | 2 |
| #26041687 | 2 |
| #26041677 | 2 |
| #26041581 | 2 |
| #26041569 | 2 |
| #26041567 | 2 |
| #26041559 | 2 |
| #26041409 | 2 |
| #26041391 | 2 |
| C4×D8×C181 | 2 |
| #3384 | 181 |