Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4 | C22×D71 |
| commutator, socle | C23×C71 | C22×C4 |
| Fitting | C2×C22⋊C8×C71 | C2 |
| hypercenter | C2×C22⋊C8 | D71 |
| hypocenter | C71 | #1955 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Dic71⋊C8 | C2 | semidirect |
| 3. C2×C22⋊(C71⋊C8) | C2 | semidirect |
| 4. C2×(C2×D71)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D71)⋊C8 | C2 | semidirect |
| 6. C2×#14556038 | C2 | semidirect |
| 7. C2×C22⋊C8×C71 | C2 | semidirect |
| 45. C2×C71⋊C8 | D4 | semidirect |
| 65. C2×C8×C71 | D4 | semidirect |
| 151. C71 | #1955 | semidirect |
| 157. C2×C22⋊C8 | D71 | semidirect |
| 211. C2×C8 | C22⋊D71 | semidirect |