Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27213544 | C2 | semidirect |
| 2. #27213526 | C2 | semidirect |
| 3. #27213497 | C2 | semidirect |
| 7. #322×C211 | C2 | semidirect |
| 68. C211 | #1720 | semidirect |
| 76. #322 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213544 | 2 |
| #27213526 | 2 |
| #27213497 | 2 |
| #27213493 | 2 |
| #322×C211 | 2 |
| #1720 | 211 |