Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26030192 | C2 | semidirect |
| 3. #26024522 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018578 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 65. C22⋊#10623494 | D4 | semidirect |
| 68. #15667919 | D4 | semidirect |
| 75. C2×C4⋊C4×C89 | D4 | semidirect |
| 76. C2×C4⋊C4×C89 | D4 | semidirect |
| 253. #1826 | D89 | semidirect |
| 257. C89 | #9940 | semidirect |
| 304. C2×C4⋊C4 | D356 | semidirect |
| 305. C2×C4⋊C4 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030192 | 2 |
| #26025178 | 2 |
| #26024522 | 2 |
| #26018782 | 2 |
| #26018578 | 2 |
| #26018105 | 2 |
| C89×#1826 | 2 |
| #9940 | 89 |