Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
260 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C211 | C2×D4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C22×C4 | C23×C211 |
| socle | C22×C211 | C2×C22⋊C4 |
| prime radical | C23×C211 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C4⋊Q8×C211 | C4 | semidirect |
| 7. C4⋊Q8×C211 | C4 | semidirect |
| 8. #125×C211 | C4 | semidirect |
| 27. M16×C211 | Q8 | semidirect |
| 81. C211 | #1986 | direct (N × H) |
| 82. #1986 | C211 | direct (N × H) |
| 88. C4⋊Q8 | C4×C211 | semidirect |
| 89. C4⋊Q8 | C4×C211 | semidirect |
| 90. #125 | C4×C211 | semidirect |
| 109. M16 | Q8×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C211 | 2 |
| C4×M16×C211 | 2 |
| C4×C4⋊C4×C211 | 2 |
| #339×C211 | 2 |
| #1986 | 211 |