Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic422 | C2 | semidirect |
| 5. #27212894 | C2 | semidirect |
| 6. #27212878 | C2 | semidirect |
| 7. Q8⋊C8×C211 | C2 | semidirect |
| 54. Dic422 | SD16 | semidirect |
| 65. Q8×C211 | SD16 | semidirect |
| 91. C211 | #1623 | semidirect |
| 99. Q8⋊C8 | D211 | semidirect |
| 148. Q8 | #16809951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic422 | 2 |
| #27213519 | 2 |
| #27213347 | 2 |
| #27213346 | 2 |
| #27212894 | 2 |
| #27212878 | 2 |
| Q8⋊C8×C211 | 2 |
| #1623 | 211 |