Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26021241 | C2 | semidirect |
| 3. #26019007 | C2 | semidirect |
| 4. #26018934 | C2 | semidirect |
| 6. M16×#10623494 | C2 | semidirect |
| 93. M16×C89 | SD16 | semidirect |
| 131. #10623494 | #100 | semidirect |
| 161. C89 | #9793 | semidirect |
| 238. M16 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151970 | 2 |
| #26021241 | 2 |
| #26019007 | 2 |
| #26018934 | 2 |
| #26018920 | 2 |
| M16×#10623494 | 2 |
| C89×#1965 | 2 |
| #9793 | 89 |