Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
222 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26018320 | C2 | semidirect |
| 4. #26018319 | C2 | semidirect |
| 5. C89×#1369 | C2 | semidirect |
| 87. D89 | #1369 | direct (N × H) |
| 92. #1369 | D89 | direct (N × H) |
| 93. C89 | C2×#1369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #364×D89 | 2 |
| #346×D89 | 2 |
| #26018320 | 2 |
| #26018319 | 2 |
| C89×#1369 | 2 |
| C2×#1369 | 89 |