Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 324 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 | C89×#3184 | C2 |
| 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×#1341 | C2 | semidirect |
| 5. C89×#1339 | C2 | semidirect |
| 7. #498×C89 | C4 | semidirect |
| 8. #493×C89 | C4 | semidirect |
| 13. #442×C89 | C4 | semidirect |
| 113. #11837 | C89 | direct (N × H) |
| 119. #2165 | C2×C89 | semidirect |
| 120. #1841 | C2×C89 | semidirect |
| 121. #1341 | C2×C89 | semidirect |
| 122. #1339 | C2×C89 | semidirect |
| 123. C89 | #11837 | direct (N × H) |
| 125. #498 | C4×C89 | semidirect |
| 126. #493 | C4×C89 | semidirect |
| 131. #442 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3184 | 2 |
| C89×#2165 | 2 |
| C89×#1841 | 2 |
| C89×#1341 | 2 |
| C89×#1339 | 2 |
| #11837 | 89 |