Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×Q16×D181 | C2 | semidirect |
| 3. #26041517 | C2 | semidirect |
| 4. #26041486 | C2 | semidirect |
| 5. #26041433 | C2 | semidirect |
| 6. C4×Dic724 | C2 | semidirect |
| 8. #494×C181 | C2 | semidirect |
| 36. Dic724 | D4 | semidirect |
| 59. D724 | Q16 | semidirect |
| 78. C2×D181 | C2×Q16 | semidirect |
| 81. C4×C181 | C2×Q16 | semidirect |
| 91. C181 | D4×Q16 | semidirect |
| 95. #494 | D181 | semidirect |
| 176. C4 | Q16×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| #26041944 | 2 |
| #26041517 | 2 |
| #26041486 | 2 |
| #26041433 | 2 |
| C4×Dic724 | 2 |
| C8×D724 | 2 |
| #494×C181 | 2 |
| D4×Q16 | 181 |