Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21454860 | C2 | semidirect |
| 2. #21444210 | C2 | semidirect |
| 3. #21444140 | C2 | semidirect |
| 4. #21443648 | C2 | semidirect |
| 28. C4×#92418 | D4 | semidirect |
| 64. C2×D4×C61 | M16 | semidirect |
| 86. C42×C61 | M16 | semidirect |
| 184. C61 | #9105 | semidirect |
| 228. C2×D4 | #11758194 | semidirect |
| 253. C42 | #11758194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454860 | 2 |
| #21444210 | 2 |
| #21444140 | 2 |
| #21443648 | 2 |
| C61×#2328 | 2 |
| #9105 | 61 |