Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1466 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1466 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23769116 | C2 | semidirect |
| 2. #23765980 | C2 | semidirect |
| 3. #23764563 | C2 | semidirect |
| 4. #23764524 | C2 | semidirect |
| 5. #23763859 | C2 | semidirect |
| 6. #23763808 | C2 | semidirect |
| 7. #23763477 | C2 | semidirect |
| 8. C79×#3491 | C2 | semidirect |
| 77. C2×C4⋊C4×C79 | D4 | semidirect |
| 78. C2×C4⋊C4×C79 | D4 | semidirect |
| 80. C2×C22⋊C4×C79 | D4 | semidirect |
| 84. C2×C42×C79 | D4 | semidirect |
| 230. #3491 | D79 | semidirect |
| 238. C79 | #23988 | semidirect |
| 298. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 299. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 307. C2×C22⋊C4 | C22⋊D79 | semidirect |
| 312. C2×C42 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769116 | 2 |
| #23765980 | 2 |
| #23764563 | 2 |
| #23764524 | 2 |
| #23763859 | 2 |
| #23763808 | 2 |
| #23763477 | 2 |
| C79×#3491 | 2 |
| #23988 | 79 |