Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
168 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #27213431 | C2 | semidirect |
| 4. #27212899 | C2 | semidirect |
| 5. #27212893 | C2 | semidirect |
| 7. #446×C211 | C2 | semidirect |
| 62. C8×C211 | SD16 | semidirect |
| 79. C211 | #1686 | semidirect |
| 84. #446 | D211 | semidirect |
| 142. C8 | #16809949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213519 | 2 |
| #27213431 | 2 |
| #27213346 | 2 |
| #27212899 | 2 |
| #27212893 | 2 |
| #27212889 | 2 |
| #446×C211 | 2 |
| #1686 | 211 |