Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C263 | C2×D4 |
| commutator | C4 | C22×C8×C263 |
| Frattini, cosocle | C2×C8 | C23×C263 |
| socle | C2×C263 | C8×D4 |
| prime radical | #135×C263 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C263 ◁ C2×C16×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #504×C263 | C2 | semidirect |
| 3. #364×C263 | C2 | semidirect |
| 4. #350×C263 | C2 | semidirect |
| 5. #346×C263 | C2 | semidirect |
| 49. C263 | #2171 | direct (N × H) |
| 50. #2171 | C263 | direct (N × H) |
| 51. #504 | C2×C263 | semidirect |
| 53. #364 | C2×C263 | semidirect |
| 54. #350 | C2×C263 | semidirect |
| 55. #346 | C2×C263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #504×C263 | 2 |
| #443×C263 | 2 |
| #364×C263 | 2 |
| #350×C263 | 2 |
| #346×C263 | 2 |
| #2171 | 263 |