Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C263 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C263 |
| prime radical | C22×D8×C263 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C263 ◁ C22×C4×C263 ◁ C22×C8×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C263 | C2 | semidirect |
| 3. C2×SD32×C263 | C2 | direct (N × H) |
| 4. C22×C16×C263 | C2 | semidirect |
| 8. C2×Q16×C263 | C22 | semidirect |
| 12. SD32×C263 | C22 | direct (N × H) |
| 13. C2×C16×C263 | C22 | semidirect |
| 22. Q16×C263 | C23 | semidirect |
| 27. C16×C263 | C23 | semidirect |
| 42. C22×C263 | SD32 | direct (N × H) |
| 48. C2×C263 | C2×SD32 | direct (N × H) |
| 50. C263 | C22×SD32 | direct (N × H) |
| 51. C22×SD32 | C263 | direct (N × H) |
| 52. C22×Q16 | C2×C263 | semidirect |
| 54. C2×SD32 | C2×C263 | direct (N × H) |
| 55. C22×C16 | C2×C263 | semidirect |
| 59. C2×Q16 | C22×C263 | semidirect |
| 63. SD32 | C22×C263 | direct (N × H) |
| 64. C2×C16 | C22×C263 | semidirect |
| 73. Q16 | C23×C263 | semidirect |
| 78. C16 | C23×C263 | semidirect |
| 93. C22 | SD32×C263 | direct (N × H) |
| 99. C2 | C2×SD32×C263 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C263 | 2 |
| C22×D8×C263 | 2 |
| C2×SD32×C263 | 2 |
| C22×C16×C263 | 2 |
| C22×SD32 | 263 |