Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
830 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ #376×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#2641 | C2 | semidirect |
| 2. C89×#2054 | C2 | semidirect |
| 3. C89×#2025 | C2 | semidirect |
| 4. C89×#2011 | C2 | semidirect |
| 5. C89×#1832 | C2 | semidirect |
| 86. #32814 | C89 | direct (N × H) |
| 91. #2641 | C2×C89 | semidirect |
| 92. #2054 | C2×C89 | semidirect |
| 93. #2025 | C2×C89 | semidirect |
| 94. #2011 | C2×C89 | semidirect |
| 95. #1832 | C2×C89 | semidirect |
| 96. C89 | #32814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2641 | 2 |
| C89×#2054 | 2 |
| C89×#2025 | 2 |
| C89×#2011 | 2 |
| C89×#1832 | 2 |
| #32814 | 89 |