Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1044 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2433 | 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 |
| 2. C89×#2435 | C2 | semidirect |
| 4. C89×#1783 | C2 | semidirect |
| 5. C89×#1508 | C2 | semidirect |
| 6. C89×#1507 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 32. C22×Q8×C89 | D4 | semidirect |
| 46. C2×M16×C89 | D4 | semidirect |
| 60. C2×C4⋊C4×C89 | D4 | semidirect |
| 79. #95×C89 | D4 | semidirect |
| 239. #10329 | C89 | direct (N × H) |
| 248. #3193 | C2×C89 | semidirect |
| 249. #2435 | C2×C89 | semidirect |
| 251. #1783 | C2×C89 | semidirect |
| 252. #1508 | C2×C89 | semidirect |
| 253. #1507 | C2×C89 | semidirect |
| 254. #1297 | C2×C89 | semidirect |
| 255. C89 | #10329 | direct (N × H) |
| 280. C22×Q8 | D4×C89 | semidirect |
| 294. C2×M16 | D4×C89 | semidirect |
| 308. C2×C4⋊C4 | D4×C89 | semidirect |
| 327. #95 | D4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3193 | 2 |
| C89×#2435 | 2 |
| C89×#2433 | 2 |
| C89×#1783 | 2 |
| C89×#1508 | 2 |
| C89×#1507 | 2 |
| C89×#1297 | 2 |
| #10329 | 89 |