Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
150 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #1347 |
| commutator | C2×C16 | C2×C4×C89 |
| Frattini, cosocle | C2×M32 | C22×C89 |
| prime radical | C89×#2218 | C2 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C2×C4×C89 ◁ C22×C8×C89 ◁ C2×M32×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1400 | C2 | semidirect |
| 3. C89×#1384 | C2 | semidirect |
| 4. C2×D16×C89 | C4 | semidirect |
| 9. #367×C89 | C4 | semidirect |
| 65. #7422 | C89 | direct (N × H) |
| 71. #1400 | C2×C89 | semidirect |
| 72. #1384 | C2×C89 | semidirect |
| 73. C89 | #7422 | direct (N × H) |
| 74. C2×D16 | C4×C89 | semidirect |
| 79. #367 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2218 | 2 |
| C89×#1400 | 2 |
| C89×#1384 | 2 |
| #7422 | 89 |