Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19153745 | C2 | semidirect |
| 4. #26041033 | C2 | semidirect |
| 25. C22⋊Dic181 | C8 | semidirect |
| 44. C2×Dic181 | C2×C8 | semidirect |
| 67. C22×C181 | C4⋊C8 | semidirect |
| 85. C181 | #1850 | semidirect |
| 153. C22 | #19153745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089678 | 2 |
| C2×#19153745 | 2 |
| C4×C22⋊Dic181 | 2 |
| #26041033 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #1850 | 181 |