Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1638 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1638 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C89 | C24 |
| commutator | C23 | C23×C4×C89 |
| Frattini, cosocle | C24 | C24×C89 |
| prime radical | C25×C89 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1443 | C2 | semidirect |
| 6. C2×#95×C89 | C4 | semidirect |
| 62. #14349 | C89 | direct (N × H) |
| 69. #1443 | C2×C89 | semidirect |
| 71. C89 | #14349 | direct (N × H) |
| 74. C2×#95 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#95×C89 | 2 |
| C89×#1443 | 2 |
| C89×C22⋊#95 | 2 |
| #14349 | 89 |