Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 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. #27213549 | C2 | semidirect |
| 2. #27213525 | C2 | semidirect |
| 6. #27212868 | C2 | semidirect |
| 7. #500×C211 | C2 | semidirect |
| 69. C211 | #1722 | semidirect |
| 72. #500 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213549 | 2 |
| #27213525 | 2 |
| #27213520 | 2 |
| #27213494 | 2 |
| #27213493 | 2 |
| #27212868 | 2 |
| #500×C211 | 2 |
| #1722 | 211 |