Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D47 |
| commutator, socle | C22×C47 | C22×C8 |
| Fitting | C47×C22⋊C16 | C2 |
| hypercenter | C22⋊C16 | D47 |
| hypocenter | C47 | #2113 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C22⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13093963 | C2 | semidirect |
| 3. C2×C16×D47 | C2 | semidirect |
| 4. C22⋊(C47⋊C16) | C2 | semidirect |
| 5. (C2×D47)⋊C16 | C2 | semidirect |
| 6. (C2×D47)⋊C16 | C2 | semidirect |
| 7. C47×C22⋊C16 | C2 | semidirect |
| 99. C22⋊C16 | D47 | semidirect |
| 100. C47 | #2113 | semidirect |