Finite Group DatabasebetaFinite Group DatabasebetaOrder 33664.
524 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C263 |
| prime radical | C22×D4×C263 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C263 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#125×C263 | C2 | semidirect |
| 3. #391×C263 | C2 | semidirect |
| 5. #388×C263 | C2 | semidirect |
| 6. C43×C263 | C2 | semidirect |
| 68. C263 | #2861 | direct (N × H) |
| 69. #2861 | C263 | direct (N × H) |
| 70. C2×#125 | C2×C263 | semidirect |
| 72. #391 | C2×C263 | semidirect |
| 74. #388 | C2×C263 | semidirect |
| 75. C43 | C2×C263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#125×C263 | 2 |
| C2×#124×C263 | 2 |
| #391×C263 | 2 |
| #390×C263 | 2 |
| #388×C263 | 2 |
| C43×C263 | 2 |
| #2861 | 263 |