Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
988 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031005 | C2 | semidirect |
| 3. #26020162 | C2 | semidirect |
| 4. #26018824 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#2848 | C2 | semidirect |
| 38. C22×#10623494 | D4 | semidirect |
| 63. C22×Q8×C89 | D4 | semidirect |
| 81. C2×C4⋊C4×C89 | D4 | semidirect |
| 87. #95×C89 | D4 | semidirect |
| 125. C24×C89 | SD16 | semidirect |
| 314. #2848 | D89 | semidirect |
| 320. C89 | #10322 | semidirect |
| 347. C22×Q8 | C22⋊D89 | semidirect |
| 380. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 400. #95 | C22⋊D89 | semidirect |
| 410. C24 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031005 | 2 |
| #26028534 | 2 |
| #26020162 | 2 |
| #26018824 | 2 |
| #26018819 | 2 |
| #26018119 | 2 |
| C89×#2848 | 2 |
| #10322 | 89 |