Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator, socle | C23×C59 | C22×C4 |
| Fitting | C59×#336 | C2 |
| hypercenter | #336 | D59 |
| hypocenter | C59 | #1870 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11745659 | C2 | semidirect |
| 3. C2×(C2×D59)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D59)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D59)⋊C8 | C2 | semidirect |
| 6. #16837157 | C2 | semidirect |
| 7. C59×#336 | C2 | semidirect |
| 54. C2×C8×C59 | D4 | semidirect |
| 65. C2×C59⋊C8 | D4 | semidirect |
| 81. C22×D59 | M16 | semidirect |
| 87. C2×C4×C59 | M16 | semidirect |
| 158. #336 | D59 | semidirect |
| 159. C59 | #1870 | semidirect |
| 213. C2×C8 | D236 | semidirect |
| 254. C2×C4 | #11745659 | semidirect |