Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19153815 | C2 | semidirect |
| 3. #26041573 | C2 | semidirect |
| 4. #26041568 | C2 | semidirect |
| 5. #26041563 | C2 | semidirect |
| 6. #26041558 | C2 | semidirect |
| 7. #26041322 | C2 | semidirect |
| 8. #26041302 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 44. #15668449 | Q8 | semidirect |
| 87. Dic362 | C2×Q8 | semidirect |
| 89. D724 | C2×Q8 | semidirect |
| 138. C181 | #3079 | semidirect |
| 147. #428 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| #26041747 | 2 |
| #26041573 | 2 |
| #26041568 | 2 |
| #26041563 | 2 |
| #26041558 | 2 |
| #26041322 | 2 |
| #26041302 | 2 |
| #26041281 | 2 |
| #26041278 | 2 |
| #428×C181 | 2 |
| #3079 | 181 |