Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C59 |
| socle | C23×C59 | C24 |
| prime radical | C24×C59 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#401 | C2 | semidirect |
| 2. C59×#400 | C2 | semidirect |
| 5. C4×C4⋊C4×C59 | C2 | semidirect |
| 7. C59×#376 | C2 | semidirect |
| 66. #2401 | C59 | direct (N × H) |
| 71. #401 | C2×C59 | semidirect |
| 72. #400 | C2×C59 | semidirect |
| 75. C4×C4⋊C4 | C2×C59 | semidirect |
| 77. #376 | C2×C59 | semidirect |
| 78. C59 | #2401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#401 | 2 |
| C59×#400 | 2 |
| C59×#397 | 2 |
| C59×#396 | 2 |
| C4×C4⋊C4×C59 | 2 |
| C4×C22⋊C4×C59 | 2 |
| C59×#376 | 2 |
| #2401 | 59 |