Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838074 | C2 | semidirect |
| 2. #16837750 | C2 | semidirect |
| 3. #16837679 | C2 | semidirect |
| 4. #16837597 | C2 | semidirect |
| 5. Q8×C59⋊C8 | C2 | semidirect |
| 6. C4×#11745669 | C2 | semidirect |
| 7. D4×Q8×C59 | C2 | semidirect |
| 47. Q8×C59 | D8 | semidirect |
| 49. D4×C59 | #41 | semidirect |
| 83. D4×Q8 | D59 | semidirect |
| 89. C59 | #3358 | semidirect |
| 129. Q8 | #11745669 | semidirect |
| 135. D4 | #11745689 | semidirect |