Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
676 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 676 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, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C2×C4×Q8×C43 | C2 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | #2548 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063314 | C2 | semidirect |
| 3. #14582816 | C2 | semidirect |
| 4. #14582801 | C2 | semidirect |
| 5. #14582800 | C2 | semidirect |
| 6. C4×C4⋊Dic43 | C2 | semidirect |
| 7. C2×C4×Q8×C43 | C2 | semidirect |
| 27. C2×Q8×C43 | D4 | semidirect |
| 88. C4×C43 | #124 | semidirect |
| 99. C2×C4×Q8 | D43 | semidirect |
| 104. C43 | #2548 | semidirect |
| 124. C2×Q8 | D172 | semidirect |
| 186. C4 | #13063314 | semidirect |