Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
118 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C89 | #357 |
| commutator | C16 | C2×C8×C89 |
| Frattini, cosocle | C4×C16 | C22×C89 |
| socle | C2×C89 | #1331 |
| prime radical | #508×C89 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C89 ◁ C2×C8×C89 ◁ C4×C8×C89 ◁ C4×C16×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1397 | C2 | semidirect |
| 3. C89×#1373 | C2 | semidirect |
| 54. #7388 | C89 | direct (N × H) |
| 59. #1397 | C2×C89 | semidirect |
| 60. #1373 | C2×C89 | semidirect |
| 61. C89 | #7388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2178 | 2 |
| C89×#1397 | 2 |
| C89×#1373 | 2 |
| #7388 | 89 |