Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1880 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×#95×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C2×#95 | D43 |
| hypocenter | C43 | C22×#95 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C43⋊#95 | C2 | semidirect |
| 3. #95×D43 | C2 | direct (N × H) |
| 4. C2×#95×C43 | C2 | semidirect |
| 8. C22×C4×D43 | C4 | semidirect |
| 10. C43⋊#95 | C22 | semidirect |
| 12. #95×C43 | C22 | semidirect |
| 19. C22×C4×C43 | C2×C4 | semidirect |
| 22. C22×Dic43 | C2×C4 | semidirect |
| 26. C2×C4×D43 | C2×C4 | semidirect |
| 39. C2×C4×C43 | C22×C4 | semidirect |
| 42. C2×Dic43 | C22×C4 | semidirect |
| 50. C2×D43 | #95 | direct (N × H) |
| 57. C2×C43 | C2×#95 | semidirect |
| 61. D43 | C2×#95 | direct (N × H) |
| 65. C2×#95 | D43 | direct (N × H) |
| 66. C43 | C22×#95 | semidirect |
| 74. #95 | C2×D43 | direct (N × H) |
| 87. C22×C4 | C4×D43 | semidirect |
| 105. C2×C4 | C2×C4×D43 | semidirect |
| 119. C2 | #95×D43 | direct (N × H) |