Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
166 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 42 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 | #1344 |
| commutator | C22×C8 | C2×C4×C89 |
| Frattini, cosocle | #408 | C22×C89 |
| prime radical | C2×#41×C89 | D4 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C2×C4×C89 ◁ C22×C4×C89 ◁ #408×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#106×C89 | C4 | semidirect |
| 10. #341×C89 | C4 | semidirect |
| 74. #7410 | C89 | direct (N × H) |
| 82. C89 | #7410 | direct (N × H) |
| 83. C2×#106 | C4×C89 | semidirect |
| 89. #341 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2079 | 2 |
| C89×#1391 | 2 |
| C89×#1321 | 2 |
| #7410 | 89 |