Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #1514 |
| commutator | C2×C8 | C22×C4×C89 |
| Frattini, cosocle | C2×M16 | C23×C89 |
| prime radical | #469×C89 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C2×C4×C89 ◁ C4×M16×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#2165 | C2 | semidirect |
| 3. C89×#1841 | C2 | semidirect |
| 4. C89×#1342 | C2 | semidirect |
| 6. C89×#1340 | C2 | semidirect |
| 9. #499×C89 | C4 | semidirect |
| 10. #495×C89 | C4 | semidirect |
| 15. #442×C89 | C4 | semidirect |
| 16. #441×C89 | C4 | semidirect |
| 135. #11836 | C89 | direct (N × H) |
| 141. #2165 | C2×C89 | semidirect |
| 142. #1841 | C2×C89 | semidirect |
| 143. #1342 | C2×C89 | semidirect |
| 145. #1340 | C2×C89 | semidirect |
| 147. C89 | #11836 | direct (N × H) |
| 149. #499 | C4×C89 | semidirect |
| 150. #495 | C4×C89 | semidirect |
| 155. #442 | C4×C89 | semidirect |
| 156. #441 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3183 | 2 |
| C89×#2165 | 2 |
| C89×#1841 | 2 |
| C89×#1342 | 2 |
| C89×#1341 | 2 |
| C89×#1340 | 2 |
| C89×#1339 | 2 |
| #11836 | 89 |