Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C43×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C43 | D47 |
| hypocenter | C47 | C4×#127 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D188 | C2 | semidirect |
| 3. #15689025 | C2 | semidirect |
| 4. #15688993 | C2 | semidirect |
| 5. C43×C47 | C2 | semidirect |
| 8. #13094021 | C4 | direct (N × H) |
| 22. C2×D188 | C2×C4 | semidirect |
| 25. C42×C47 | C2×C4 | semidirect |
| 26. C42×C47 | D4 | semidirect |
| 49. C4×C47 | C4×D4 | semidirect |
| 50. C4×C47 | #127 | semidirect |
| 61. C43 | D47 | semidirect |
| 62. C47 | C4×#127 | semidirect |
| 84. C42 | C4×D47 | semidirect |
| 85. C42 | D188 | semidirect |
| 107. C4 | C4×D188 | semidirect |
| 108. C4 | #13094021 | direct (N × H) |