Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
150 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C42 | C23×C211 |
| socle | C22×C211 | C2×C4⋊C4 |
| prime radical | C23×C211 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ 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 |
|---|---|---|
| 4. #335×C211 | C2 | semidirect |
| 5. #334×C211 | C2 | semidirect |
| 56. C211 | #1572 | direct (N × H) |
| 57. #1572 | C211 | direct (N × H) |
| 61. #335 | C2×C211 | semidirect |
| 62. #334 | C2×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #432×C211 | 2 |
| #431×C211 | 2 |
| #335×C211 | 2 |
| #334×C211 | 2 |
| #1572 | 211 |