Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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×#20269913 | C2 | semidirect |
| 4. #27212910 | C2 | semidirect |
| 5. C2×#108×C211 | C2 | semidirect |
| 69. C2×D211 | #108 | semidirect |
| 80. C211 | #1810 | semidirect |
| 84. C2×#108 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D211 | 2 |
| C2×#20269913 | 2 |
| #27213109 | 2 |
| #27212910 | 2 |
| C2×#108×C211 | 2 |
| #1810 | 211 |