Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273696 |
| commutator | C23×C59 | C24 |
| Frattini | C23 | C23×D59 |
| Fitting | C59×#585 | C2 |
| socle | C2×C59 | C2×#120 |
| hypercenter | #585 | D59 |
| hypocenter | C59 | #3025 |
| LCS | G ▷ C23×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837909 | C2 | semidirect |
| 2. #16837592 | C2 | semidirect |
| 3. #16837589 | C2 | semidirect |
| 4. #16837376 | C2 | semidirect |
| 5. C59×#585 | C2 | semidirect |
| 6. C22×C4×D59 | C22 | semidirect |
| 7. #14273708 | C22 | semidirect |
| 10. #14273695 | C22 | semidirect |
| 12. #14273686 | C22 | semidirect |
| 13. #14273642 | C22 | semidirect |
| 26. C2×Q8×C59 | D4 | semidirect |
| 29. C2×D4×C59 | D4 | semidirect |
| 32. C22×C4×C59 | D4 | semidirect |
| 83. #585 | D59 | semidirect |
| 88. C59 | #3025 | semidirect |
| 109. C2×Q8 | C22⋊D59 | semidirect |
| 113. C2×D4 | C22⋊D59 | semidirect |
| 119. C22×C4 | C22⋊D59 | semidirect |