Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837843 | C2 | direct (N × H) |
| 3. C2×#14273673 | C2 | semidirect |
| 4. C2×#14273670 | C2 | semidirect |
| 5. C2×#14273667 | C2 | semidirect |
| 6. C22×Q16×C59 | C2 | semidirect |
| 13. #14273673 | C22 | semidirect |
| 14. #14273670 | C22 | semidirect |
| 15. #14273667 | C22 | semidirect |
| 21. C2×Q16×C59 | C22 | semidirect |
| 81. C2×C59 | #510 | semidirect |
| 85. C22×Q16 | D59 | semidirect |
| 90. C59 | C2×#510 | semidirect |
| 99. C2×Q16 | C2×D59 | semidirect |
| 165. C2 | #16837843 | direct (N × H) |