Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
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. C22×Dic172 | C2 | semidirect |
| 3. #14583342 | C2 | direct (N × H) |
| 4. C2×Dic344 | C2 | semidirect |
| 5. C2×#13063270 | C2 | semidirect |
| 6. C2×M32×C43 | C2 | semidirect |
| 15. C2×Dic172 | C22 | semidirect |
| 18. Dic344 | C22 | semidirect |
| 19. #13063270 | C22 | semidirect |
| 21. M32×C43 | C22 | semidirect |
| 81. C2×C43 | #510 | semidirect |
| 89. C2×M32 | D43 | semidirect |
| 90. C43 | C2×#510 | semidirect |
| 105. M32 | C2×D43 | semidirect |
| 165. C2 | #14583342 | direct (N × H) |