Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
736 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C89 |
| prime radical | C2×#127×C89 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#3185 | C2 | semidirect |
| 3. C89×#1720 | C2 | semidirect |
| 4. C89×#1711 | C2 | semidirect |
| 5. C89×#1455 | C2 | semidirect |
| 8. #498×C89 | C22 | semidirect |
| 9. #494×C89 | C22 | semidirect |
| 11. #487×C89 | C22 | semidirect |
| 18. #322×C89 | C22 | semidirect |
| 19. C82×C89 | C22 | semidirect |
| 74. #19753 | C89 | direct (N × H) |
| 78. #3185 | C2×C89 | semidirect |
| 80. #1720 | C2×C89 | semidirect |
| 81. #1711 | C2×C89 | semidirect |
| 82. #1455 | C2×C89 | semidirect |
| 83. C89 | #19753 | direct (N × H) |
| 86. #498 | C22×C89 | semidirect |
| 87. #494 | C22×C89 | semidirect |
| 89. #487 | C22×C89 | semidirect |
| 96. #322 | C22×C89 | semidirect |
| 97. C82 | C22×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3185 | 2 |
| C89×#3138 | 2 |
| C89×#1720 | 2 |
| C89×#1711 | 2 |
| C89×#1455 | 2 |
| #19753 | 89 |