Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1664 conjugacy classes of subgroups; only the 941 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 941 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C22×C4⋊C4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C22×C4⋊C4 | D59 |
| hypocenter | C59 | C22×C4×Q8 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273692 | C2 | direct (N × H) |
| 7. C22×Dic118 | C4 | semidirect |
| 12. #14273692 | C22 | direct (N × H) |
| 26. C22×Dic59 | Q8 | semidirect |
| 30. C2×Dic118 | C2×C4 | semidirect |
| 46. C2×Dic59 | C2×Q8 | semidirect |
| 50. Dic118 | C22×C4 | semidirect |
| 51. C22×C59 | C4×Q8 | semidirect |
| 60. Dic59 | C22×Q8 | semidirect |
| 62. C2×C59 | C2×C4×Q8 | semidirect |
| 72. C59 | C22×C4×Q8 | semidirect |
| 117. C22 | #14273692 | direct (N × H) |
| 127. C2 | C2×#14273692 | direct (N × H) |