Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#99 |
| commutator | C24 | C22×C4×C61 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C61 |
| prime radical | C25×C61 | C2×C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C24×C61 ◁ C22×C22⋊C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C61×#1326 | C2 | semidirect |
| 5. C61×#1317 | C2 | semidirect |
| 154. #11543 | C61 | direct (N × H) |
| 191. #1326 | C2×C61 | semidirect |
| 192. #1317 | C2×C61 | semidirect |
| 219. C61 | #11543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2483 | 2 |
| C61×#1462 | 2 |
| C2×C61×#323 | 2 |
| C61×#1326 | 2 |
| C61×#1317 | 2 |
| #11543 | 61 |