Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27213338 | C2 | semidirect |
| 2. #27213225 | C2 | semidirect |
| 3. #27212897 | C2 | semidirect |
| 4. #27212890 | C2 | semidirect |
| 5. #493×C211 | C2 | semidirect |
| 50. C8×C211 | D8 | semidirect |
| 68. C211 | #1687 | semidirect |
| 70. #493 | D211 | semidirect |
| 119. C8 | #16809947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213338 | 2 |
| #27213225 | 2 |
| #27212897 | 2 |
| #27212890 | 2 |
| #493×C211 | 2 |
| #1687 | 211 |