Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×C16×D181 | C2 | semidirect |
| 3. #26041058 | C2 | semidirect |
| 4. C4×#15668424 | C2 | semidirect |
| 5. C4⋊C16×C181 | C2 | semidirect |
| 23. #15668424 | D4 | semidirect |
| 29. D724 | C16 | semidirect |
| 43. C2×D181 | C2×C16 | semidirect |
| 45. C4×C181 | C2×C16 | semidirect |
| 53. C181 | D4×C16 | semidirect |
| 57. C4⋊C16 | D181 | semidirect |
| 100. C4 | C16×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D181 | 2 |
| C8×D724 | 2 |
| #26041058 | 2 |
| C4×#15668424 | 2 |
| C4⋊C16×C181 | 2 |
| D4×C16 | 181 |