Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D47 |
| commutator | C2×C47 | C22×C16 |
| Frattini | C2×C8 | C22×D47 |
| Fitting | C4×C16×C47 | C2 |
| socle | C22×C47 | C22×C8 |
| hypercenter | C4×C16 | D47 |
| hypocenter | C47 | D4×C16 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C16 ◁ C4×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C16×D47 | C2 | semidirect |
| 3. C4⋊(C47⋊C16) | C2 | semidirect |
| 4. (C2×D47)⋊C16 | C2 | semidirect |
| 5. C4×C16×C47 | C2 | semidirect |
| 26. C16×C47 | D4 | semidirect |
| 33. D188 | C16 | direct (N × H) |
| 43. C2×D47 | C2×C16 | semidirect |
| 45. C4×C47 | C2×C16 | semidirect |
| 58. C4×C16 | D47 | semidirect |
| 59. C47 | D4×C16 | semidirect |
| 81. C16 | D188 | direct (N × H) |
| 100. C4 | C16×D47 | semidirect |