Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C277 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C277 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C277 ◁ C42×C277 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 81. C277 | #1636 | direct (N × H) |
| 82. #1636 | C277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #557×C277 | 2 |
| #487×C277 | 2 |
| #477×C277 | 2 |
| #332×C277 | 2 |
| Q8⋊C8×C277 | 2 |
| #1636 | 277 |