Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063298 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#410 | C2 |
| socle | C2×C43 | #386 |
| hypercenter | #410 | D43 |
| hypocenter | C43 | #1906 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #410 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583367 | C2 | semidirect |
| 3. #14582917 | C2 | semidirect |
| 4. C2×#13063252 | C2 | semidirect |
| 5. #14582669 | C2 | semidirect |
| 6. #14582658 | C2 | semidirect |
| 7. C43×#410 | C2 | semidirect |
| 9. #13063356 | C4 | semidirect |
| 11. #13063351 | C4 | semidirect |
| 33. C2×Q8×C43 | C2×C4 | semidirect |
| 35. C2×D4×C43 | C2×C4 | semidirect |
| 67. #10621877 | C2×C4 | semidirect |
| 134. #410 | D43 | semidirect |
| 137. C43 | #1906 | semidirect |
| 168. C2×Q8 | C4×D43 | semidirect |
| 172. C2×D4 | C4×D43 | semidirect |