Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#19153835 | C2 | semidirect |
| 2. C2×#19153761 | C2 | semidirect |
| 3. C2×#19153757 | C2 | semidirect |
| 4. #26041516 | C2 | semidirect |
| 5. #26041082 | C2 | semidirect |
| 6. #26041058 | C2 | semidirect |
| 7. #357×C181 | C2 | semidirect |
| 32. Dic724 | D4 | semidirect |
| 43. D8×C181 | D4 | semidirect |
| 89. C181 | #2186 | semidirect |
| 96. #357 | D181 | semidirect |
| 128. D8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| C2×#19153761 | 2 |
| C2×#19153757 | 2 |
| #26041516 | 2 |
| #26041082 | 2 |
| #26041058 | 2 |
| #357×C181 | 2 |
| #2186 | 181 |