Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
846 conjugacy classes of subgroups; only the 394 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 394 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #8813 |
| commutator | C82 | C22×C3×C4 |
| Frattini, cosocle | C2×C82 | C23×C3 |
| prime radical | C23×C3 | #1705 |
| LCS | G ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C82 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #72214006 | C3 | direct (N × H) |
| 10. C3×#7052 | C4 | semidirect |
| 11. C3×C162 | C4 | semidirect |
| 30. #7052 | C3×C4 | semidirect |
| 31. C162 | C3×C4 | semidirect |
| 92. C3×C16 | #365 | semidirect |
| 125. C16 | C3×#365 | semidirect |
| 146. C3 | #72214006 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#122211 | 2 |
| C3×#135792 | 2 |
| C3×#135758 | 2 |
| #72214006 | 3 |