Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D43 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#340 | C2 |
| socle | C23×C43 | C2×D4 |
| hypercenter | #340 | D43 |
| hypocenter | C43 | #1999 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D344 | C2 | semidirect |
| 2. C2×#13063300 | C2 | semidirect |
| 3. C2×#13063245 | C2 | semidirect |
| 4. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 5. C43×#340 | C2 | semidirect |
| 32. C2×D172 | D4 | semidirect |
| 38. C2×C8×C43 | D4 | semidirect |
| 40. C4⋊C4×C43 | D4 | semidirect |
| 57. C22×D43 | D8 | semidirect |
| 111. #340 | D43 | semidirect |
| 112. C43 | #1999 | semidirect |
| 148. C2×C8 | D172 | semidirect |
| 150. C4⋊C4 | D172 | semidirect |