Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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×C59 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C59 |
| prime radical | C2×D4×C59 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#494 | C2 | semidirect |
| 4. C59×#334 | C2 | semidirect |
| 5. C59×#332 | C2 | semidirect |
| 57. #1689 | C59 | direct (N × H) |
| 62. #494 | C2×C59 | semidirect |
| 65. #334 | C2×C59 | semidirect |
| 66. #332 | C2×C59 | semidirect |
| 67. C59 | #1689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#494 | 2 |
| C59×#474 | 2 |
| C59×#436 | 2 |
| C59×#334 | 2 |
| C59×#332 | 2 |
| #1689 | 59 |