Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
170 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 70 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×C547 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C547 |
| prime radical | C24×C547 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C547 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊C4×C547 | C2 | semidirect |
| 4. #95×C547 | C2 | semidirect |
| 5. #95×C547 | C2 | semidirect |
| 50. C547 | #397 | direct (N × H) |
| 51. #397 | C547 | direct (N × H) |
| 52. C2×C4⋊C4 | C2×C547 | semidirect |
| 55. #95 | C2×C547 | semidirect |
| 56. #95 | C2×C547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C547 | 2 |
| C2×C22⋊C4×C547 | 2 |
| #95×C547 | 2 |
| #397 | 547 |