Order 6016.
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×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C2×#117×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#117 | D47 |
| hypocenter | C47 | #2309 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13093983 | C2 | semidirect |
| 3. #15689025 | C2 | semidirect |
| 4. #15689024 | C2 | semidirect |
| 5. #15688978 | C2 | semidirect |
| 6. C2×#117×C47 | C2 | semidirect |
| 10. C22×D188 | C4 | semidirect |
| 14. C2×C4⋊Dic47 | C22 | semidirect |
| 16. C2×(C2×D47)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic47 | C22 | semidirect |
| 20. C2×C4⋊C4×C47 | C22 | semidirect |
| 22. C2×C42×C47 | C22 | semidirect |
| 65. C2×C4×C47 | C22⋊C4 | semidirect |
| 102. C2×#117 | D47 | semidirect |
| 106. C47 | #2309 | semidirect |
| 117. C2×C4⋊C4 | C2×D47 | semidirect |
| 122. C2×C42 | C2×D47 | semidirect |
| 169. C2×C4 | (C2×D47)⋊C4 | semidirect |