Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
792 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C89 |
| prime radical | C89×#3006 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C23×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#3193 | C2 | semidirect |
| 3. C89×#2616 | C2 | semidirect |
| 4. C89×#1964 | C2 | semidirect |
| 5. C89×#1789 | C2 | semidirect |
| 6. C89×#1508 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 259. #9931 | C89 | direct (N × H) |
| 269. #3193 | C2×C89 | semidirect |
| 271. #2616 | C2×C89 | semidirect |
| 272. #1964 | C2×C89 | semidirect |
| 273. #1789 | C2×C89 | semidirect |
| 274. #1508 | C2×C89 | semidirect |
| 275. #1305 | C2×C89 | semidirect |
| 276. C89 | #9931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3193 | 2 |
| C89×#3006 | 2 |
| C89×#2616 | 2 |
| C89×#1964 | 2 |
| C89×#1789 | 2 |
| C89×#1508 | 2 |
| C89×#1305 | 2 |
| #9931 | 89 |