Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041641 | C2 | semidirect |
| 3. #26041631 | C2 | semidirect |
| 4. #26041627 | C2 | semidirect |
| 5. #26041278 | C2 | semidirect |
| 6. C4×#15668433 | C2 | semidirect |
| 7. C2×C4⋊Q8×C181 | C2 | semidirect |
| 100. C181 | #3141 | semidirect |
| 103. C2×C4⋊Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041641 | 2 |
| #26041631 | 2 |
| #26041627 | 2 |
| #26041278 | 2 |
| C4×#15668433 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| #3141 | 181 |