Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
436 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C71 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C71 |
| prime radical | C24×C71 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #400×C71 | C2 | semidirect |
| 2. #398×C71 | C2 | semidirect |
| 72. #2646 | C71 | direct (N × H) |
| 73. C71 | #2646 | direct (N × H) |
| 74. #400 | C2×C71 | semidirect |
| 75. #398 | C2×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #400×C71 | 2 |
| #398×C71 | 2 |
| #385×C71 | 2 |
| #380×C71 | 2 |
| C2×#95×C71 | 2 |
| #2646 | 71 |