Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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, socle | C23×C47 | C24 |
| Fitting | C4×C4⋊C4×C47 | C2 |
| hypercenter | C4×C4⋊C4 | D47 |
| hypocenter | C47 | #2662 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094018 | C2 | semidirect |
| 2. C2×#13094012 | C2 | semidirect |
| 3. #15689045 | C2 | semidirect |
| 4. #15689044 | C2 | semidirect |
| 5. #15689041 | C2 | semidirect |
| 6. #15689040 | C2 | semidirect |
| 7. #15689036 | C2 | semidirect |
| 9. #15689025 | C2 | semidirect |
| 10. #15689014 | C2 | semidirect |
| 11. C4×C4⋊C4×C47 | C2 | semidirect |
| 57. C42×C47 | D4 | semidirect |
| 154. C4×C4⋊C4 | D47 | semidirect |
| 155. C47 | #2662 | semidirect |
| 214. C42 | D188 | semidirect |