Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#19153814 | C2 | semidirect |
| 4. #26041186 | C2 | semidirect |
| 5. #26041184 | C2 | semidirect |
| 6. #26041174 | C2 | semidirect |
| 7. #26041148 | C2 | semidirect |
| 36. C22×Dic181 | Q8 | semidirect |
| 99. C22×C181 | C4⋊Q8 | semidirect |
| 112. Dic181 | C22⋊Q8 | semidirect |
| 119. C181 | #2857 | semidirect |
| 219. C22 | #19153814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153814 | 2 |
| C2×#19153795 | 2 |
| C22×C4×Dic181 | 2 |
| #26041186 | 2 |
| #26041184 | 2 |
| #26041174 | 2 |
| #26041148 | 2 |
| #26041137 | 2 |
| C2×C22⋊Q8×C181 | 2 |
| #2857 | 181 |