Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153816 | C2 | semidirect |
| 3. #26041575 | C2 | semidirect |
| 4. #26041570 | C2 | semidirect |
| 5. #26041565 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 9. #423×C181 | C2 | semidirect |
| 36. #15668449 | Q8 | semidirect |
| 74. Dic362 | C2×Q8 | semidirect |
| 76. D724 | C2×Q8 | semidirect |
| 121. C181 | #3079 | semidirect |
| 130. #423 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153816 | 2 |
| C4×#15668449 | 2 |
| #26041575 | 2 |
| #26041570 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #26041321 | 2 |
| #26041281 | 2 |
| #423×C181 | 2 |
| #3079 | 181 |