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×#19153839 | C2 | semidirect |
| 2. C2×#19153759 | C2 | semidirect |
| 3. C2×D2896 | C2 | semidirect |
| 4. #26041516 | C2 | semidirect |
| 5. #26041079 | C2 | semidirect |
| 6. #26041058 | C2 | semidirect |
| 7. #358×C181 | C2 | semidirect |
| 35. D1448 | D4 | semidirect |
| 43. Q16×C181 | D4 | semidirect |
| 89. C181 | #2186 | semidirect |
| 95. #358 | D181 | semidirect |
| 123. Q16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153759 | 2 |
| C2×D2896 | 2 |
| #26041516 | 2 |
| #26041079 | 2 |
| #26041058 | 2 |
| #358×C181 | 2 |
| #2186 | 181 |