Order 5504.
1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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 | C22×C43 | C23×C4 |
| Fitting | C2×#117×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | #2309 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063284 | C2 | semidirect |
| 3. #14582801 | C2 | semidirect |
| 4. #14582800 | C2 | semidirect |
| 5. #14582754 | C2 | semidirect |
| 6. C2×#117×C43 | C2 | semidirect |
| 10. C22×D172 | C4 | semidirect |
| 14. C2×C4⋊Dic43 | C22 | semidirect |
| 16. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic43 | C22 | semidirect |
| 20. C2×C4⋊C4×C43 | C22 | semidirect |
| 22. C2×C42×C43 | C22 | semidirect |
| 65. C2×C4×C43 | C22⋊C4 | semidirect |
| 102. C2×#117 | D43 | semidirect |
| 106. C43 | #2309 | semidirect |
| 117. C2×C4⋊C4 | C2×D43 | semidirect |
| 122. C2×C42 | C2×D43 | semidirect |
| 169. C2×C4 | (C2×D43)⋊C4 | semidirect |