Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
248 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 124 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×C263 | C22⋊C4 |
| commutator | C22 | C22×C8×C263 |
| Frattini, cosocle | C22×C4 | C23×C263 |
| socle | C22×C263 | C2×C22⋊C4 |
| prime radical | C23×C263 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C263 ◁ C2×C42×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C2×Q8×C263 | C8 | semidirect |
| 61. C263 | #1461 | direct (N × H) |
| 62. #1461 | C263 | direct (N × H) |
| 78. C2×Q8 | C8×C263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C263 | 2 |
| #431×C263 | 2 |
| #324×C263 | 2 |
| #1461 | 263 |