Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D59 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#340 | C2 |
| socle | C23×C59 | C2×D4 |
| hypercenter | #340 | D59 |
| hypocenter | C59 | #2074 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 111. C59 | #2074 | semidirect |