Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
126 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C59 |
| prime radical | #135×C59 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#498 | C2 | semidirect |
| 3. C59×#365 | C2 | semidirect |
| 4. C59×#364 | C2 | semidirect |
| 17. Q16×C59 | Q8 | semidirect |
| 19. D8×C59 | Q8 | semidirect |
| 49. #2230 | C59 | direct (N × H) |
| 53. #498 | C2×C59 | semidirect |
| 55. #365 | C2×C59 | semidirect |
| 56. #364 | C2×C59 | semidirect |
| 58. C59 | #2230 | direct (N × H) |
| 70. Q16 | Q8×C59 | semidirect |
| 72. D8 | Q8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#498 | 2 |
| C59×#443 | 2 |
| C59×#365 | 2 |
| C59×#364 | 2 |
| C59×#360 | 2 |
| #2230 | 59 |