Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D61 |
| commutator, socle, cosocle | C23×C61 | C25 |
| Fitting | C61×#2868 | C2 |
| hypercenter | #2868 | D61 |
| hypocenter | C61 | #36644 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16840313 | C2 | semidirect |
| 2. #21454214 | C2 | semidirect |
| 3. #21454177 | C2 | semidirect |
| 4. #21454165 | C2 | semidirect |
| 5. #21448381 | C2 | semidirect |
| 6. C43×D61 | C2 | semidirect |
| 7. C61×#2868 | C2 | semidirect |
| 40. C42×D61 | D4 | semidirect |
| 65. C42×C61 | #41 | semidirect |
| 88. C4×D61 | #127 | semidirect |
| 98. C4×C61 | #532 | semidirect |
| 102. #2868 | D61 | semidirect |
| 127. C61 | #36644 | semidirect |
| 174. C42 | #11758226 | semidirect |
| 204. C4 | #16840313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840313 | 2 |
| #21454214 | 2 |
| #21454177 | 2 |
| #21454165 | 2 |
| #21448381 | 2 |
| C43×D61 | 2 |
| C61×#2868 | 2 |
| #36644 | 61 |