Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
310 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | #124×C89 | C2 |
| hypercenter | #124 | D89 |
| hypocenter | C89 | #532 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13083575 | C2 | semidirect |
| 2. C2×#13083573 | C2 | semidirect |
| 3. #15668010 | C2 | semidirect |
| 4. #15668008 | C2 | semidirect |
| 5. #15668000 | C2 | semidirect |
| 6. #15667985 | C2 | semidirect |
| 7. #15667972 | C2 | semidirect |
| 8. C42×D89 | C2 | semidirect |
| 9. #124×C89 | C2 | semidirect |
| 47. C4×D89 | D4 | semidirect |
| 61. Dic89 | #41 | semidirect |
| 67. C89 | #532 | semidirect |
| 74. #124 | D89 | semidirect |