Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C61×#2184 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C61×#424 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3262 | C2 | semidirect |
| 2. C61×#2187 | C2 | semidirect |
| 4. C61×#2045 | C2 | semidirect |
| 5. C61×#1350 | C2 | semidirect |
| 6. C61×#1349 | C2 | semidirect |
| 7. C61×#1323 | C2 | semidirect |
| 140. #12166 | C61 | direct (N × H) |
| 161. #3262 | C2×C61 | semidirect |
| 162. #2187 | C2×C61 | semidirect |
| 164. #2045 | C2×C61 | semidirect |
| 165. #1350 | C2×C61 | semidirect |
| 166. #1349 | C2×C61 | semidirect |
| 167. #1323 | C2×C61 | semidirect |
| 193. C61 | #12166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3262 | 2 |
| C61×#2187 | 2 |
| C61×#2184 | 2 |
| C61×#2045 | 2 |
| C61×#1350 | 2 |
| C61×#1349 | 2 |
| C61×#1323 | 2 |
| #12166 | 61 |