Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1688 | C2 | semidirect |
| 2. C2×#20269952 | C2 | semidirect |
| 3. C2×#20269897 | C2 | semidirect |
| 4. C2×(C2×D211)⋊C8 | C2 | semidirect |
| 5. #340×C211 | C2 | semidirect |
| 29. C2×D844 | D4 | semidirect |
| 42. C2×C8×C211 | D4 | semidirect |
| 44. C4⋊C4×C211 | D4 | semidirect |
| 56. C22×D211 | D8 | semidirect |
| 106. C211 | #1999 | semidirect |
| 112. #340 | D211 | semidirect |
| 148. C2×C8 | D844 | semidirect |
| 150. C4⋊C4 | D844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1688 | 2 |
| C2×#20269952 | 2 |
| C2×#20269897 | 2 |
| C2×(C2×D211)⋊C8 | 2 |
| #340×C211 | 2 |
| #1999 | 211 |