Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×#20269909 | C2 | semidirect |
| 3. C2×#20269902 | C2 | semidirect |
| 5. #27213052 | C2 | semidirect |
| 7. C2×C4×C8×C211 | C2 | semidirect |
| 12. C2×#16809951 | C4 | semidirect |
| 79. C2×C4×C211 | SD16 | semidirect |
| 87. C8×C211 | C22⋊C4 | semidirect |
| 112. C211 | #1968 | semidirect |
| 118. C2×C4×C8 | D211 | semidirect |
| 192. C2×C4 | #16809951 | semidirect |
| 200. C8 | (C2×D211)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809951 | 2 |
| C2×#20269909 | 2 |
| C2×#20269902 | 2 |
| C2×#20269899 | 2 |
| #27213052 | 2 |
| #27213048 | 2 |
| C2×C4×C8×C211 | 2 |
| #1968 | 211 |