Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
182 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 182 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 | C59×#459 | C2 |
| 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×#492 | C2 | semidirect |
| 2. C59×#474 | C2 | semidirect |
| 4. C59×#436 | C2 | semidirect |
| 5. C59×#335 | C2 | semidirect |
| 6. C59×#332 | C2 | semidirect |
| 7. C59×#331 | C2 | semidirect |
| 65. C8×C59 | D8 | semidirect |
| 80. #1685 | C59 | direct (N × H) |
| 86. #492 | C2×C59 | semidirect |
| 87. #474 | C2×C59 | semidirect |
| 89. #436 | C2×C59 | semidirect |
| 90. #335 | C2×C59 | semidirect |
| 91. #332 | C2×C59 | semidirect |
| 92. #331 | C2×C59 | semidirect |
| 93. C59 | #1685 | direct (N × H) |
| 151. C8 | D8×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#492 | 2 |
| C59×#474 | 2 |
| C59×#459 | 2 |
| C59×#436 | 2 |
| C59×#335 | 2 |
| C59×#332 | 2 |
| C59×#331 | 2 |
| #1685 | 59 |