Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
140 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #102 |
| commutator | C8 | C42×C211 |
| Frattini, cosocle | C22×C8 | C22×C211 |
| prime radical | C23×C211 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ C22×C4×C211 ◁ C22×C8×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. M32×C211 | C4 | semidirect |
| 10. #107×C211 | C4 | semidirect |
| 13. #106×C211 | C4 | semidirect |
| 56. C211 | #1386 | direct (N × H) |
| 57. #1386 | C211 | direct (N × H) |
| 65. M32 | C4×C211 | semidirect |
| 67. #107 | C4×C211 | semidirect |
| 70. #106 | C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M32×C211 | 2 |
| #427×C211 | 2 |
| C2×#106×C211 | 2 |
| #1386 | 211 |