Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C22×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#3486 | C2 | semidirect |
| 2. C89×#3020 | C2 | semidirect |
| 3. C89×#2010 | C2 | semidirect |
| 4. C89×#1912 | C2 | semidirect |
| 5. C89×#1784 | C2 | semidirect |
| 39. C4⋊Q8×C89 | D4 | semidirect |
| 41. #124×C89 | D4 | semidirect |
| 145. #23899 | C89 | direct (N × H) |
| 151. #3486 | C2×C89 | semidirect |
| 152. #3020 | C2×C89 | semidirect |
| 153. #2010 | C2×C89 | semidirect |
| 154. #1912 | C2×C89 | semidirect |
| 155. #1784 | C2×C89 | semidirect |
| 156. C89 | #23899 | direct (N × H) |
| 190. C4⋊Q8 | D4×C89 | semidirect |
| 192. #124 | D4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3486 | 2 |
| C89×#3020 | 2 |
| C89×#2010 | 2 |
| C89×#1912 | 2 |
| C89×#1784 | 2 |
| #23899 | 89 |