Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | D236 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C43×C59 | C2 |
| socle | C22×C59 | C2×C22⋊C4 |
| hypercenter | C43 | D59 |
| hypocenter | C59 | C4×#104 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#11745664 | C2 | semidirect |
| 4. #16837162 | C2 | semidirect |
| 5. C43×C59 | C2 | semidirect |
| 8. C4×Dic118 | C4 | semidirect |
| 9. C4×D236 | C4 | semidirect |
| 14. #14273655 | C4 | direct (N × H) |
| 33. C42×C59 | C2×C4 | semidirect |
| 43. #11745664 | C2×C4 | semidirect |
| 60. D236 | C42 | semidirect |
| 64. Dic118 | C42 | semidirect |
| 73. C4×C59 | #104 | semidirect |
| 87. C43 | D59 | semidirect |
| 89. C59 | C4×#104 | semidirect |
| 126. C42 | C4×D59 | semidirect |
| 159. C4 | #14273655 | direct (N × H) |