Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | D172 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C23×C8×C43 | C2 |
| socle | C24×C43 | D4 |
| hypercenter | C23×C8 | D43 |
| hypocenter | C43 | C22×#103 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13063250 | C2 | direct (N × H) |
| 7. C22×Dic86 | C4 | semidirect |
| 13. #13063250 | C22 | direct (N × H) |
| 29. C2×Dic86 | C2×C4 | semidirect |
| 50. Dic86 | C22×C4 | semidirect |
| 52. C22×C43 | #103 | semidirect |
| 63. C2×C43 | C2×#103 | semidirect |
| 71. C43 | C22×#103 | semidirect |
| 119. C22 | #13063250 | direct (N × H) |
| 129. C2 | C2×#13063250 | direct (N × H) |