Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1616 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1616 conjugacy classes of subgroups — too many to draw. Only its 242 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C61 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3459 | C2 | semidirect |
| 2. C61×#2408 | C2 | semidirect |
| 3. C61×#2029 | C2 | semidirect |
| 4. C61×#2021 | C2 | semidirect |
| 5. C61×#1799 | C2 | semidirect |
| 30. C23×C4×C61 | D4 | semidirect |
| 52. C2×C4⋊C4×C61 | D4 | semidirect |
| 56. C2×C22⋊C4×C61 | D4 | semidirect |
| 59. C2×C42×C61 | D4 | semidirect |
| 156. #29684 | C61 | direct (N × H) |
| 182. #3459 | C2×C61 | semidirect |
| 183. #2408 | C2×C61 | semidirect |
| 184. #2029 | C2×C61 | semidirect |
| 185. #2021 | C2×C61 | semidirect |
| 186. #1799 | C2×C61 | semidirect |
| 211. C61 | #29684 | direct (N × H) |
| 219. C23×C4 | D4×C61 | semidirect |
| 241. C2×C4⋊C4 | D4×C61 | semidirect |
| 245. C2×C22⋊C4 | D4×C61 | semidirect |
| 248. C2×C42 | D4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3459 | 2 |
| C61×#2408 | 2 |
| C61×#2029 | 2 |
| C61×#2021 | 2 |
| C61×#1799 | 2 |
| #29684 | 61 |