Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #26041026 | C2 | semidirect |
| 5. #26041025 | C2 | semidirect |
| 6. #26041024 | C2 | semidirect |
| 7. #332×C181 | C2 | semidirect |
| 91. D181 | #332 | direct (N × H) |
| 92. C181 | C2×#332 | semidirect |
| 100. #332 | D181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D181 | 2 |
| C4⋊C8×D181 | 2 |
| #26041026 | 2 |
| #26041025 | 2 |
| #26041024 | 2 |
| #332×C181 | 2 |
| C2×#332 | 181 |