Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
216 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C42 | C23×C211 |
| prime radical | C23×C211 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #333×C211 | C2 | semidirect |
| 5. #332×C211 | C2 | semidirect |
| 79. C211 | #1550 | direct (N × H) |
| 80. #1550 | C211 | direct (N × H) |
| 84. #333 | C2×C211 | semidirect |
| 85. #332 | C2×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C211 | 2 |
| #423×C211 | 2 |
| C2×C4⋊C8×C211 | 2 |
| #333×C211 | 2 |
| #332×C211 | 2 |
| #1550 | 211 |