Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D71 |
| commutator, socle | C22×C71 | C22×C8 |
| Fitting | C22×C16×C71 | C2 |
| hypercenter | C22×C16 | D71 |
| hypocenter | C71 | #2168 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556067 | C2 | semidirect |
| 3. Dic71⋊C16 | C2 | semidirect |
| 4. C22⋊(C71⋊C16) | C2 | semidirect |
| 5. (C2×D71)⋊C16 | C2 | semidirect |
| 6. #17985774 | C2 | semidirect |
| 7. C22×C16×C71 | C2 | semidirect |
| 39. C16×C71 | D4 | semidirect |
| 59. C22×C71 | M32 | semidirect |
| 76. C71 | #2168 | semidirect |
| 78. C22×C16 | D71 | semidirect |
| 115. C16 | C22⋊D71 | semidirect |
| 138. C22 | #14556067 | semidirect |