Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 130 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 | #102×C89 | C2 |
| socle | C22×C89 | C2×D4 |
| hypercenter | #102 | D89 |
| hypocenter | C89 | #469 |
| LCS | G ▷ C2×C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13083559 | C2 | semidirect |
| 2. C2×#13083557 | C2 | semidirect |
| 3. #15667987 | C2 | semidirect |
| 4. #15667983 | C2 | semidirect |
| 5. #15667943 | C2 | semidirect |
| 6. #15667934 | C2 | semidirect |
| 7. #102×C89 | C2 | semidirect |
| 37. #10623494 | D4 | semidirect |
| 59. C89 | #469 | semidirect |
| 67. #102 | D89 | semidirect |