Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 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×C211 | #95 |
| commutator | C2×C4 | C42×C211 |
| Frattini, cosocle | C2×C42 | C22×C211 |
| prime radical | C23×C211 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #97×C211 | C4 | semidirect |
| 10. C4×C8×C211 | C4 | semidirect |
| 55. C211 | #1288 | direct (N × H) |
| 56. #1288 | C211 | direct (N × H) |
| 65. #97 | C4×C211 | semidirect |
| 66. C4×C8 | C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #432×C211 | 2 |
| C4×M16×C211 | 2 |
| #383×C211 | 2 |
| #1288 | 211 |