Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#10620273 | C2 | semidirect |
| 3. #13050152 | C2 | semidirect |
| 4. C4×D164 | C2 | semidirect |
| 5. #13050089 | C2 | semidirect |
| 6. #13050086 | C2 | semidirect |
| 7. C4⋊C8×C41 | C2 | semidirect |
| 56. C41 | #463 | semidirect |
| 61. C4⋊C8 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620273 | 2 |
| C2×D328 | 2 |
| #13050152 | 2 |
| C4×D164 | 2 |
| #13050089 | 2 |
| #13050086 | 2 |
| C4⋊C8×C41 | 2 |
| #463 | 41 |