Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
116 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 44 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 | C2×C8 | C2×C4×C211 |
| Frattini, cosocle | C22×C8 | C22×C211 |
| prime radical | C23×C211 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×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 |
|---|---|---|
| 4. C2×Q16×C211 | C4 | semidirect |
| 9. #107×C211 | C4 | semidirect |
| 54. C211 | #1348 | direct (N × H) |
| 55. #1348 | C211 | direct (N × H) |
| 59. C2×Q16 | C4×C211 | semidirect |
| 64. #107 | C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×C211 | 2 |
| C22⋊C16×C211 | 2 |
| #340×C211 | 2 |
| #1348 | 211 |