Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
152 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×D4 |
| commutator | C2×C4 | C22×C4×C59 |
| Frattini, cosocle | C42 | C23×C59 |
| socle, prime radical | C22×C59 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C4×C8×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 40. C8×C59 | Q16 | semidirect |
| 49. #1591 | C59 | direct (N × H) |
| 58. C59 | #1591 | direct (N × H) |
| 93. C8 | Q16×C59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#446 | 2 |
| C4×Q16×C59 | 2 |
| C59×#335 | 2 |
| C59×Q8⋊C8 | 2 |
| C82×C59 | 2 |
| #1591 | 59 |