Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#427 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #427 | D43 |
| hypocenter | C43 | #2943 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583367 | C2 | semidirect |
| 3. #14583010 | C2 | semidirect |
| 4. #14583005 | C2 | semidirect |
| 5. #14582998 | C2 | semidirect |
| 6. #14582893 | C2 | semidirect |
| 7. C2×#13063235 | C2 | semidirect |
| 8. C43×#427 | C2 | semidirect |
| 10. #13063347 | C4 | semidirect |
| 33. #10621898 | C2×C4 | semidirect |
| 38. C2×C8×C43 | C2×C4 | semidirect |
| 51. Dic172 | C2×C4 | semidirect |
| 52. D344 | C2×C4 | semidirect |
| 53. #10621873 | C2×C4 | semidirect |
| 95. #427 | D43 | semidirect |
| 98. C43 | #2943 | semidirect |
| 133. C2×C8 | C4×D43 | semidirect |