Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 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 |
| 2. C2×#10620272 | C2 | semidirect |
| 3. #13050144 | C2 | semidirect |
| 5. #13050087 | C2 | semidirect |
| 6. #13050084 | C2 | semidirect |
| 7. #107×C41 | C2 | semidirect |
| 35. C8×C41 | D4 | semidirect |
| 56. C41 | #468 | semidirect |
| 61. #107 | D41 | semidirect |
| 92. C8 | D164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620273 | 2 |
| C2×#10620272 | 2 |
| #13050144 | 2 |
| #13050139 | 2 |
| #13050087 | 2 |
| #13050084 | 2 |
| #107×C41 | 2 |
| #468 | 41 |