Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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 | C47×#390 | C2 |
| hypercenter | #390 | D47 |
| hypocenter | C47 | #2555 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094010 | C2 | semidirect |
| 2. C2×#13093997 | C2 | semidirect |
| 3. #15689043 | C2 | semidirect |
| 4. #15689040 | C2 | semidirect |
| 5. #15689031 | C2 | semidirect |
| 6. #15689011 | C2 | semidirect |
| 7. #15688999 | C2 | semidirect |
| 8. C4×(C2×D47)⋊C4 | C2 | semidirect |
| 9. C47×#390 | C2 | semidirect |
| 66. (C2×D47)⋊C4 | D4 | semidirect |
| 148. #390 | D47 | semidirect |
| 152. C47 | #2555 | semidirect |