Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#446 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #446 | D59 |
| hypocenter | C59 | #3384 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ #446 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838112 | C2 | semidirect |
| 2. Q8×D236 | C2 | semidirect |
| 3. #16837811 | C2 | semidirect |
| 4. #16837800 | C2 | semidirect |
| 5. #16837703 | C2 | semidirect |
| 6. #16837693 | C2 | semidirect |
| 7. #16837693 | C2 | semidirect |
| 8. #16837683 | C2 | semidirect |
| 11. C59×#446 | C2 | semidirect |
| 72. D472 | Q8 | semidirect |
| 88. D236 | C2×Q8 | semidirect |
| 98. C8×C59 | C2×Q8 | semidirect |
| 130. #446 | D59 | semidirect |
| 133. C59 | #3384 | semidirect |
| 220. C8 | Q8×D59 | semidirect |