Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C211 | #121 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C22×C4 | C23×C211 |
| socle | C2×C211 | #390 |
| prime radical | C2×#135×C211 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C211 ◁ C22×C4×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #427×C211 | C2 | semidirect |
| 3. #421×C211 | C2 | semidirect |
| 4. #410×C211 | C2 | semidirect |
| 5. #405×C211 | C2 | semidirect |
| 11. C2×Q16×C211 | C4 | semidirect |
| 12. C2×SD16×C211 | C4 | semidirect |
| 13. C2×D8×C211 | C4 | semidirect |
| 96. C211 | #1976 | direct (N × H) |
| 97. #1976 | C211 | direct (N × H) |
| 99. #427 | C2×C211 | semidirect |
| 100. #421 | C2×C211 | semidirect |
| 101. #410 | C2×C211 | semidirect |
| 102. #405 | C2×C211 | semidirect |
| 108. C2×Q16 | C4×C211 | semidirect |
| 109. C2×SD16 | C4×C211 | semidirect |
| 110. C2×D8 | C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C211 | 2 |
| #427×C211 | 2 |
| #421×C211 | 2 |
| #410×C211 | 2 |
| #405×C211 | 2 |
| #1976 | 211 |