Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C71 |
| prime radical | #459×C71 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C42×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #486×C71 | C2 | semidirect |
| 2. #461×C71 | C2 | semidirect |
| 4. #436×C71 | C2 | semidirect |
| 5. #334×C71 | C2 | semidirect |
| 6. #332×C71 | C2 | semidirect |
| 7. #331×C71 | C2 | semidirect |
| 84. #1701 | C71 | direct (N × H) |
| 85. C71 | #1701 | direct (N × H) |
| 86. #486 | C2×C71 | semidirect |
| 87. #461 | C2×C71 | semidirect |
| 89. #436 | C2×C71 | semidirect |
| 90. #334 | C2×C71 | semidirect |
| 91. #332 | C2×C71 | semidirect |
| 92. #331 | C2×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #486×C71 | 2 |
| #461×C71 | 2 |
| #459×C71 | 2 |
| #436×C71 | 2 |
| #334×C71 | 2 |
| #332×C71 | 2 |
| #331×C71 | 2 |
| #1701 | 71 |