Finite Group DatabasebetaFinite Group DatabasebetaOrder 5696.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D356 |
| commutator | C4×C89 | C22×C4 |
| Frattini | C2×C4 | C22×D89 |
| Fitting | C2×M16×C89 | C2 |
| socle | C22×C89 | C2×D4 |
| hypercenter | C2×M16 | D89 |
| hypocenter | C89 | #417 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊Dic89 | C2 | semidirect |
| 3. #15667937 | C2 | semidirect |
| 4. #15667934 | C2 | semidirect |
| 5. C2×M16×C89 | C2 | semidirect |
| 7. #13083574 | C4 | semidirect |
| 29. D356 | C2×C4 | semidirect |
| 32. Dic178 | C2×C4 | semidirect |
| 51. C89 | #417 | semidirect |
| 54. C2×M16 | D89 | semidirect |