Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. #26018379 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 5. C89×#1394 | C2 | semidirect |
| 13. #101×D89 | C4 | semidirect |
| 46. #15667931 | C2×C4 | semidirect |
| 56. #101×C89 | C2×C4 | semidirect |
| 197. D89 | #1394 | direct (N × H) |
| 202. #1394 | D89 | direct (N × H) |
| 203. C89 | C2×#1394 | semidirect |
| 251. #101 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#101×D89 | 2 |
| #391×D89 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1394 | 2 |
| C2×#1394 | 89 |