Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19153755 | C2 | semidirect |
| 3. C4⋊#15668424 | C2 | semidirect |
| 4. #26041058 | C2 | semidirect |
| 5. C4×C16×C181 | C2 | semidirect |
| 27. C16×C181 | D4 | semidirect |
| 45. C4×C181 | M32 | semidirect |
| 53. C181 | #2169 | semidirect |
| 59. C4×C16 | D181 | semidirect |
| 81. C16 | D724 | semidirect |
| 100. C4 | #19153755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153755 | 2 |
| C8×D724 | 2 |
| C4⋊#15668424 | 2 |
| #26041058 | 2 |
| C4×C16×C181 | 2 |
| #2169 | 181 |