Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
304 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 128 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×C263 | C2×D4 |
| commutator | C2×C4 | C22×C4×C263 |
| Frattini, cosocle | C22×C4 | C23×C263 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C263 ◁ C2×C42×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×Q16×C263 | C4 | semidirect |
| 74. C263 | #1971 | direct (N × H) |
| 75. #1971 | C263 | direct (N × H) |
| 84. C2×Q16 | C4×C263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C263 | 2 |
| C2×#106×C263 | 2 |
| C2×#103×C263 | 2 |
| C2×#97×C263 | 2 |
| #391×C263 | 2 |
| #1971 | 263 |