Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
1072 conjugacy classes of subgroups; only the 520 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 520 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C263 | C22 |
| commutator | C2 | C23×C8×C263 |
| Frattini, cosocle | C2×C4 | C24×C263 |
| socle | C24×C263 | C2×C4 |
| prime radical | C25×C263 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C8×C263 | C2 | semidirect |
| 3. C2×C22⋊C8×C263 | C2 | direct (N × H) |
| 11. C22×C8×C263 | C22 | semidirect |
| 12. C22⋊C8×C263 | C22 | direct (N × H) |
| 15. C24×C263 | C8 | semidirect |
| 28. C2×C8×C263 | C23 | semidirect |
| 34. C23×C263 | C2×C8 | semidirect |
| 50. C22×C263 | C22⋊C8 | direct (N × H) |
| 53. C22×C263 | C22×C8 | semidirect |
| 60. C2×C263 | C2×C22⋊C8 | direct (N × H) |
| 64. C263 | C22×C22⋊C8 | direct (N × H) |
| 65. C22×C22⋊C8 | C263 | direct (N × H) |
| 67. C23×C8 | C2×C263 | semidirect |
| 68. C2×C22⋊C8 | C2×C263 | direct (N × H) |
| 76. C22×C8 | C22×C263 | semidirect |
| 77. C22⋊C8 | C22×C263 | direct (N × H) |
| 80. C24 | C8×C263 | semidirect |
| 93. C2×C8 | C23×C263 | semidirect |
| 99. C23 | C2×C8×C263 | semidirect |
| 115. C22 | C22⋊C8×C263 | direct (N × H) |
| 118. C22 | C22×C8×C263 | semidirect |
| 125. C2 | C2×C22⋊C8×C263 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C263 | 2 |
| C23×C8×C263 | 2 |
| C2×C22⋊C8×C263 | 2 |
| C22×C22⋊C8 | 263 |