Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16840197 | C2 | semidirect |
| 2. #21455467 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. #21447555 | C2 | semidirect |
| 5. #21447447 | C2 | semidirect |
| 6. #21443933 | C2 | semidirect |
| 7. C61×#3067 | C2 | semidirect |
| 48. #14519717 | D4 | semidirect |
| 65. C2×Q16×C61 | D4 | semidirect |
| 67. C2×D8×C61 | D4 | semidirect |
| 78. #108×C61 | D4 | semidirect |
| 206. #3067 | D61 | semidirect |
| 242. C61 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D61 | semidirect |
| 263. C2×D8 | C22⋊D61 | 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×#16840197 | 2 |
| #21455467 | 2 |
| C2×#16839574 | 2 |
| #21447555 | 2 |
| #21447447 | 2 |
| #21443933 | 2 |
| C61×#3067 | 2 |
| #13310 | 61 |