Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
278 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#19153752 | C2 | semidirect |
| 4. #26041044 | C2 | semidirect |
| 71. C22×C181 | #108 | semidirect |
| 85. C181 | #1855 | semidirect |
| 157. C22 | #19153752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668433 | 2 |
| C2×#19153752 | 2 |
| #26041243 | 2 |
| #26041044 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #1855 | 181 |