Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. D4×Dic362 | C2 | semidirect |
| 2. #26041944 | C2 | semidirect |
| 3. #26041683 | C2 | semidirect |
| 4. #26041682 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041558 | C2 | semidirect |
| 7. #26041557 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 51. #15668434 | Q8 | semidirect |
| 78. Dic362 | D8 | semidirect |
| 80. D724 | C2×Q8 | semidirect |
| 89. #13089678 | C2×Q8 | semidirect |
| 93. D4×C181 | C2×Q8 | semidirect |
| 123. C181 | Q8×D8 | semidirect |
| 132. #474 | D181 | semidirect |
| 208. D4 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic362 | 2 |
| #26041944 | 2 |
| #26041683 | 2 |
| #26041682 | 2 |
| #26041560 | 2 |
| #26041558 | 2 |
| #26041557 | 2 |
| #26041403 | 2 |
| C4×#15668434 | 2 |
| #26041359 | 2 |
| #474×C181 | 2 |
| Q8×D8 | 181 |