Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
370 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C277 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C277 |
| prime radical | #537×C277 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C277 ◁ C22×C4×C277 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#137×C277 | C2 | semidirect |
| 3. C2×#104×C277 | C2 | semidirect |
| 4. #391×C277 | C2 | semidirect |
| 5. #343×C277 | C2 | semidirect |
| 28. C2×Q8×C277 | D4 | semidirect |
| 40. M16×C277 | D4 | semidirect |
| 93. C277 | #2007 | direct (N × H) |
| 94. #2007 | C277 | direct (N × H) |
| 95. C2×#137 | C2×C277 | semidirect |
| 97. C2×#104 | C2×C277 | semidirect |
| 98. #391 | C2×C277 | semidirect |
| 99. #343 | C2×C277 | semidirect |
| 122. C2×Q8 | D4×C277 | semidirect |
| 134. M16 | D4×C277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C277 | 2 |
| #537×C277 | 2 |
| C2×#104×C277 | 2 |
| #391×C277 | 2 |
| #343×C277 | 2 |
| #2007 | 277 |