Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 3. #19151556 | C2 | semidirect |
| 4. #19151553 | C2 | semidirect |
| 5. M16×Dic89 | C2 | semidirect |
| 6. C2×C8×Dic89 | C2 | semidirect |
| 8. #15668019 | C4 | semidirect |
| 21. #131×C89 | C4 | semidirect |
| 25. #13083558 | C2×C4 | semidirect |
| 26. C2×#10623494 | C2×C4 | semidirect |
| 39. M16×C89 | C2×C4 | semidirect |
| 40. C2×C8×C89 | C2×C4 | semidirect |
| 64. Dic89 | #131 | direct (N × H) |
| 69. C89 | C4×#131 | semidirect |
| 79. #131 | Dic89 | direct (N × H) |
| 100. M16 | C2×Dic89 | semidirect |
| 104. C2×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668019 | 2 |
| #41×Dic89 | 2 |
| #19151556 | 2 |
| #19151553 | 2 |
| M16×Dic89 | 2 |
| C2×C8×Dic89 | 2 |
| C2×#131×C89 | 2 |
| C4×#131 | 89 |