Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
328 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C131 | #99 |
| commutator | C22×C4 | C42×C131 |
| Frattini, cosocle | C2×#117 | C22×C131 |
| socle | C22×C131 | #342 |
| prime radical | C24×C131 | C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 143. #7253 | C131 | direct (N × H) |
| 144. C131 | #7253 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1798×C131 | 2 |
| #1742×C131 | 2 |
| #1458×C131 | 2 |
| #7253 | 131 |