Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#20269901 | C2 | semidirect |
| 4. #27212901 | C2 | semidirect |
| 5. C2×C4⋊Q8×C211 | C2 | semidirect |
| 61. C2×C4×C211 | SD16 | semidirect |
| 87. C211 | #2013 | semidirect |
| 90. C2×C4⋊Q8 | D211 | semidirect |
| 148. C2×C4 | #16809949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809949 | 2 |
| C2×#20269901 | 2 |
| #27213048 | 2 |
| #27212901 | 2 |
| C2×C4⋊Q8×C211 | 2 |
| #2013 | 211 |