Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
172 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C211 | C22⋊C4 |
| commutator | C2×C4 | C42×C211 |
| Frattini, cosocle | C2×C42 | C22×C211 |
| socle | C22×C211 | #95 |
| prime radical | C23×C211 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C4⋊C8×C211 | C4 | semidirect |
| 10. #97×C211 | C4 | semidirect |
| 56. C211 | #1300 | direct (N × H) |
| 57. #1300 | C211 | direct (N × H) |
| 64. C4⋊C8 | C4×C211 | semidirect |
| 67. #97 | 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 |
| #376×C211 | 2 |
| #1300 | 211 |