Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
780 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C61 |
| prime radical | C2×#121×C61 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C61×#2434 | C2 | semidirect |
| 4. C61×#1784 | C2 | semidirect |
| 5. C61×#1508 | C2 | semidirect |
| 7. C61×#1297 | C2 | semidirect |
| 191. #10330 | C61 | direct (N × H) |
| 219. #2434 | C2×C61 | semidirect |
| 220. #1784 | C2×C61 | semidirect |
| 221. #1508 | C2×C61 | semidirect |
| 223. #1297 | C2×C61 | semidirect |
| 254. C61 | #10330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3193 | 2 |
| C61×#2436 | 2 |
| C61×#2434 | 2 |
| C61×#1784 | 2 |
| C61×#1508 | 2 |
| C61×#1507 | 2 |
| C61×#1297 | 2 |
| #10330 | 61 |