Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C47 | C22×C42 |
| Fitting | C2×#95×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#95 | D47 |
| hypocenter | C47 | #2275 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15688974 | C2 | semidirect |
| 3. C4×C22⋊Dic47 | C2 | semidirect |
| 4. #15688970 | C2 | semidirect |
| 5. #15688968 | C2 | semidirect |
| 6. #95×D47 | C2 | semidirect |
| 7. C2×#95×C47 | C2 | semidirect |
| 10. C4×C22⋊D47 | C4 | semidirect |
| 24. C22×C4×C47 | C2×C4 | semidirect |
| 32. C2×C4×D47 | C2×C4 | semidirect |
| 33. C22⋊Dic47 | C2×C4 | semidirect |
| 34. (C2×D47)⋊C4 | C2×C4 | semidirect |
| 35. Dic47⋊C4 | C2×C4 | semidirect |
| 37. C4×Dic47 | C2×C4 | semidirect |
| 50. C22⋊D47 | C42 | semidirect |
| 84. C2×#95 | D47 | semidirect |
| 85. C47 | #2275 | semidirect |
| 108. C22×C4 | C4×D47 | semidirect |