Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#20270002 | C2 | semidirect |
| 2. C22×D1688 | C2 | semidirect |
| 3. C2×#20269893 | C2 | semidirect |
| 4. #27212911 | C2 | semidirect |
| 5. #408×C211 | C2 | semidirect |
| 84. C211 | #2018 | semidirect |
| 89. #408 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20270002 | 2 |
| C22×D1688 | 2 |
| C2×#20269893 | 2 |
| #27212911 | 2 |
| #408×C211 | 2 |
| #2018 | 211 |