Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 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×#102 |
| 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 |
|---|---|---|
| 2. C22×C4⋊Dic43 | C2 | semidirect |
| 3. C2×#13063247 | C2 | direct (N × H) |
| 4. C23×C8×C43 | C2 | semidirect |
| 8. C22×D172 | C4 | semidirect |
| 12. C2×C4⋊Dic43 | C22 | semidirect |
| 13. #13063247 | C22 | direct (N × H) |
| 16. C22×C8×C43 | C22 | semidirect |
| 31. C2×D172 | C2×C4 | semidirect |
| 34. C2×C8×C43 | C23 | semidirect |
| 36. C4⋊Dic43 | C23 | semidirect |
| 55. D172 | C22×C4 | semidirect |
| 57. C22×C43 | #102 | semidirect |
| 71. C2×C43 | C2×#102 | semidirect |
| 77. C23×C8 | D43 | semidirect |
| 80. C43 | C22×#102 | semidirect |
| 89. C22×C8 | C2×D43 | semidirect |
| 110. C2×C8 | C22×D43 | semidirect |
| 137. C22 | #13063247 | direct (N × H) |
| 147. C2 | C2×#13063247 | direct (N × H) |