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 |
| 4. #26041658 | C2 | semidirect |
| 5. #26041519 | C2 | semidirect |
| 6. #26041490 | C2 | semidirect |
| 7. #26041436 | C2 | semidirect |
| 8. #26041433 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 57. #15668439 | D4 | semidirect |
| 89. D724 | Q16 | semidirect |
| 114. C2×D181 | C2×Q16 | semidirect |
| 119. C4×C181 | C2×Q16 | semidirect |
| 130. C181 | D4×Q16 | semidirect |
| 138. #462 | D181 | semidirect |
| 254. 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 |
| Q8×D724 | 2 |
| #26041944 | 2 |
| #26041658 | 2 |
| #26041519 | 2 |
| #26041490 | 2 |
| #26041436 | 2 |
| #26041433 | 2 |
| C4×#15668439 | 2 |
| #26041344 | 2 |
| #462×C181 | 2 |
| D4×Q16 | 181 |