Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Fitting | C43×#336 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | C2×#336 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582654 | C2 | semidirect |
| 4. #14582653 | C2 | semidirect |
| 5. C43×#336 | C2 | semidirect |
| 11. C2×C8×D43 | C4 | semidirect |
| 24. C2×C4×D43 | C8 | semidirect |
| 31. C2×C8×C43 | C2×C4 | semidirect |
| 37. C2×C43⋊C8 | C2×C4 | semidirect |
| 47. C2×C4×C43 | C2×C8 | semidirect |
| 57. C2×Dic43 | C2×C8 | semidirect |
| 84. D43 | #336 | direct (N × H) |
| 89. #336 | D43 | direct (N × H) |
| 90. C43 | C2×#336 | semidirect |
| 120. C2×C8 | C4×D43 | semidirect |
| 141. C2×C4 | C8×D43 | semidirect |