Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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×#20269974 | C2 | semidirect |
| 3. C2×#20269899 | C2 | semidirect |
| 4. #27213048 | C2 | semidirect |
| 5. #336×C211 | C2 | semidirect |
| 32. C2×D844 | D4 | semidirect |
| 41. C2×C8×C211 | D4 | semidirect |
| 65. C2×C4×C211 | D8 | semidirect |
| 97. C211 | #2011 | semidirect |
| 103. #336 | D211 | semidirect |
| 137. C2×C8 | D844 | semidirect |
| 163. C2×C4 | D1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1688 | 2 |
| C2×#20269974 | 2 |
| C2×#20269899 | 2 |
| #27213048 | 2 |
| #336×C211 | 2 |
| #2011 | 211 |