Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16840198 | C2 | semidirect |
| 2. #21455540 | C2 | semidirect |
| 3. #21455463 | C2 | semidirect |
| 4. #21447556 | C2 | semidirect |
| 5. #21447446 | C2 | semidirect |
| 6. #21443933 | C2 | semidirect |
| 7. C2×C61×#361 | C2 | semidirect |
| 42. C2×Dic244 | D4 | semidirect |
| 44. C2×D488 | D4 | semidirect |
| 60. #14519717 | D4 | semidirect |
| 80. #108×C61 | D4 | semidirect |
| 208. C2×#361 | D61 | semidirect |
| 242. C61 | #13310 | semidirect |
| 287. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840198 | 2 |
| #21455540 | 2 |
| #21455463 | 2 |
| #21447556 | 2 |
| #21447446 | 2 |
| #21443933 | 2 |
| C2×C61×#361 | 2 |
| #13310 | 61 |