Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #26041587 | C2 | semidirect |
| 4. #26041575 | C2 | semidirect |
| 5. #26041565 | C2 | semidirect |
| 37. C2×Dic362 | Q8 | semidirect |
| 106. C181 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| C2×C4×Dic362 | 2 |
| #26041587 | 2 |
| #26041575 | 2 |
| #26041565 | 2 |
| #26041321 | 2 |
| #26041289 | 2 |
| #423×C181 | 2 |
| #3078 | 181 |