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×#16840203 | C2 | semidirect |
| 3. C2×#16840017 | C2 | semidirect |
| 4. C2×#16839573 | C2 | semidirect |
| 5. C2×#16839543 | C2 | semidirect |
| 6. #21443924 | C2 | semidirect |
| 7. C61×#2141 | C2 | semidirect |
| 60. #14519717 | D4 | semidirect |
| 63. #14519709 | D4 | semidirect |
| 73. C2×Q16×C61 | D4 | semidirect |
| 210. #2141 | D61 | semidirect |
| 242. C61 | #13317 | semidirect |
| 256. C2×Q16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840203 | 2 |
| #21455429 | 2 |
| C2×#16840017 | 2 |
| C2×#16839573 | 2 |
| C2×#16839543 | 2 |
| #21443924 | 2 |
| C61×#2141 | 2 |
| #13317 | 61 |