Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 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 | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×#95×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C2×#95 | D43 |
| hypocenter | C43 | C2×#381 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582761 | C2 | direct (N × H) |
| 4. C2×C43⋊#95 | C2 | semidirect |
| 5. C2×C43⋊#95 | C2 | semidirect |
| 6. C2×#95×C43 | C2 | semidirect |
| 11. C22×C4×D43 | C4 | semidirect |
| 15. C43⋊#95 | C22 | semidirect |
| 16. C43⋊#95 | C22 | semidirect |
| 19. #95×C43 | C22 | semidirect |
| 43. C2×C4×D43 | C2×C4 | semidirect |
| 97. C2×C43 | #381 | semidirect |
| 109. C2×#95 | D43 | semidirect |
| 110. C43 | C2×#381 | semidirect |
| 123. #95 | C2×D43 | semidirect |
| 201. C2 | #14582761 | direct (N × H) |