Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C211 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C42 | C23×C211 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #332×C211 | C2 | direct (N × H) |
| 71. C2×C211 | #332 | direct (N × H) |
| 75. C211 | C2×#332 | direct (N × H) |
| 76. C2×#332 | C211 | direct (N × H) |
| 80. #332 | C2×C211 | direct (N × H) |
| 147. C2 | #332×C211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Q8×C211 | 2 |
| C2×C4⋊C8×C211 | 2 |
| #332×C211 | 2 |
| C2×#332 | 211 |