Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C89×#2733 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#2093 | C2 | semidirect |
| 3. C89×#2072 | C2 | semidirect |
| 4. C89×#2071 | C2 | semidirect |
| 5. C89×#1272 | C2 | semidirect |
| 6. C89×#1270 | C2 | semidirect |
| 7. C89×#1270 | C2 | semidirect |
| 205. #7796 | C89 | direct (N × H) |
| 216. #2093 | C2×C89 | semidirect |
| 217. #2072 | C2×C89 | semidirect |
| 218. #2071 | C2×C89 | semidirect |
| 219. #1272 | C2×C89 | semidirect |
| 220. #1270 | C2×C89 | semidirect |
| 221. #1270 | C2×C89 | semidirect |
| 222. C89 | #7796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2733 | 2 |
| C89×#2093 | 2 |
| C89×#2072 | 2 |
| C89×#2071 | 2 |
| C89×#1272 | 2 |
| C89×#1270 | 2 |
| #7796 | 89 |