Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22626738 | C2 | semidirect |
| 2. #22625228 | C2 | semidirect |
| 3. C2×#17989435 | C2 | semidirect |
| 4. #22625172 | C2 | semidirect |
| 5. #22624777 | C2 | semidirect |
| 6. #22624764 | C2 | semidirect |
| 103. C2×D292 | M16 | semidirect |
| 134. M16×C73 | M16 | semidirect |
| 233. C73 | #9097 | semidirect |
| 340. M16 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626738 | 2 |
| #22625228 | 2 |
| C2×#17989435 | 2 |
| #22625172 | 2 |
| #22624777 | 2 |
| #22624764 | 2 |
| #22618738 | 2 |
| #9097 | 73 |