Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
826 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 182 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×C131 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C131 |
| Frattini, cosocle | C2×C42 | C23×C131 |
| prime radical | C24×C131 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#330×C131 | C2 | semidirect |
| 90. C22×C131 | #330 | semidirect |
| 107. #8335 | C131 | direct (N × H) |
| 108. C131 | #8335 | direct (N × H) |
| 111. C2×#330 | C2×C131 | semidirect |
| 198. C22 | #330×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#125×C131 | 2 |
| #1749×C131 | 2 |
| C2×#330×C131 | 2 |
| #8335 | 131 |