Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19153756 | C2 | semidirect |
| 3. #26041060 | C2 | direct (N × H) |
| 4. C2×M32×C181 | C2 | semidirect |
| 14. #19153756 | C22 | semidirect |
| 18. M32×C181 | C22 | semidirect |
| 82. C2×C181 | #349 | semidirect |
| 85. C181 | C2×#349 | semidirect |
| 89. C2×M32 | D181 | semidirect |
| 103. M32 | C2×D181 | semidirect |
| 169. C2 | #26041060 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×#19153756 | 2 |
| #26041060 | 2 |
| C2×M32×C181 | 2 |
| C2×#349 | 181 |