Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D89 |
| commutator | C2×C4×C89 | C23 |
| Frattini | C2×C4 | C22×D89 |
| Fitting | #106×C89 | C2 |
| socle | C22×C89 | C2×D4 |
| hypercenter | #106 | D89 |
| hypocenter | C89 | #481 |
| LCS | G ▷ C2×C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #106 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊C4×D89 | C2 | semidirect |
| 3. #15667943 | C2 | semidirect |
| 4. #15667934 | C2 | semidirect |
| 5. #15667932 | C2 | semidirect |
| 6. #15667924 | C2 | semidirect |
| 7. #106×C89 | C2 | semidirect |
| 52. C89 | #481 | semidirect |
| 57. #106 | D89 | semidirect |