Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
928 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C4×C22⋊C4×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C4×C22⋊C4 | D71 |
| hypocenter | C71 | #2339 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D284 | C2 | semidirect |
| 3. #17985905 | C2 | semidirect |
| 4. #17985875 | C2 | semidirect |
| 5. #17985861 | C2 | semidirect |
| 6. #17985859 | C2 | semidirect |
| 7. #95×D71 | C2 | semidirect |
| 8. C4×C22⋊C4×C71 | C2 | semidirect |
| 10. C2×#11765865 | C4 | semidirect |
| 31. C2×Dic142 | C2×C4 | semidirect |
| 35. C2×C22⋊D71 | C2×C4 | semidirect |
| 42. C2×C4×D71 | C2×C4 | semidirect |
| 48. C22×C4×C71 | C2×C4 | semidirect |
| 76. C2×C4×C71 | #41 | semidirect |
| 83. D284 | C22⋊C4 | semidirect |
| 116. C71 | #2339 | semidirect |
| 123. C4×C22⋊C4 | D71 | semidirect |
| 161. C22×C4 | C4×D71 | semidirect |
| 202. C2×C4 | #11765865 | semidirect |