Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
252 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C71 |
| Frattini, cosocle | C42 | C23×C71 |
| prime radical | #532×C71 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #432×C71 | C2 | semidirect |
| 3. C2×C4⋊C8×C71 | C2 | semidirect |
| 4. #333×C71 | C2 | semidirect |
| 5. #331×C71 | C2 | semidirect |
| 84. #1551 | C71 | direct (N × H) |
| 85. C71 | #1551 | direct (N × H) |
| 87. #432 | C2×C71 | semidirect |
| 88. C2×C4⋊C8 | C2×C71 | semidirect |
| 89. #333 | C2×C71 | semidirect |
| 90. #331 | C2×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C71 | 2 |
| #432×C71 | 2 |
| C2×C4⋊C8×C71 | 2 |
| #333×C71 | 2 |
| #331×C71 | 2 |
| #1551 | 71 |