Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
336 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C211 | C2×D4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C22×C4 | C23×C211 |
| prime radical | C24×C211 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C211 ◁ C23×C4×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#107×C211 | C2 | semidirect |
| 4. #340×C211 | C2 | semidirect |
| 7. C22×C8×C211 | C4 | semidirect |
| 49. C8×C211 | C22⋊C4 | semidirect |
| 54. C22×C211 | #107 | semidirect |
| 71. C211 | #1808 | direct (N × H) |
| 72. #1808 | C211 | direct (N × H) |
| 74. C2×#107 | C2×C211 | semidirect |
| 76. #340 | C2×C211 | semidirect |
| 79. C22×C8 | C4×C211 | semidirect |
| 121. C8 | C22⋊C4×C211 | semidirect |
| 126. C22 | #107×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C211 | 2 |
| C2×#107×C211 | 2 |
| #380×C211 | 2 |
| #340×C211 | 2 |
| #1808 | 211 |