Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13050163 | C2 | semidirect |
| 2. #13050162 | C2 | semidirect |
| 3. #13050154 | C2 | semidirect |
| 7. C4×Dic82 | C2 | semidirect |
| 8. C4×Dic82 | C2 | semidirect |
| 11. C4×Q8×C41 | C2 | semidirect |
| 49. C4×D41 | Q8 | semidirect |
| 71. C41 | #533 | semidirect |
| 80. C4×Q8 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050163 | 2 |
| #13050162 | 2 |
| #13050154 | 2 |
| #13050144 | 2 |
| #13050142 | 2 |
| #13050140 | 2 |
| C4×Dic82 | 2 |
| #13050121 | 2 |
| C42×D41 | 2 |
| C4×Q8×C41 | 2 |
| #533 | 41 |