Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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. #26041683 | C2 | semidirect |
| 3. #26041680 | C2 | semidirect |
| 4. #26041679 | C2 | semidirect |
| 5. #26041676 | C2 | semidirect |
| 31. C2×#13089678 | Q8 | semidirect |
| 44. C2×C8×C181 | Q8 | semidirect |
| 78. C181 | #3160 | semidirect |
| 114. C2×C8 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| #26041683 | 2 |
| #26041680 | 2 |
| #26041679 | 2 |
| #26041676 | 2 |
| #26041317 | 2 |
| #26041315 | 2 |
| C2×C8×Dic181 | 2 |
| #427×C181 | 2 |
| #3160 | 181 |