Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27213184 | C2 | semidirect |
| 2. #27213163 | C2 | semidirect |
| 3. #27213120 | C2 | semidirect |
| 4. #27213101 | C2 | semidirect |
| 20. C2×Q16×C211 | C4 | semidirect |
| 21. C2×SD16×C211 | C4 | semidirect |
| 22. C2×D8×C211 | C4 | semidirect |
| 96. C211 | #1976 | semidirect |
| 108. C2×Q16 | Dic211 | semidirect |
| 109. C2×SD16 | Dic211 | semidirect |
| 110. C2×D8 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213184 | 2 |
| #27213163 | 2 |
| #27213120 | 2 |
| #27213101 | 2 |
| C2×#135×C211 | 2 |
| #1976 | 211 |