Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. M64×D73 | C2 | semidirect |
| 3. #368×D73 | C2 | semidirect |
| 4. #22608124 | C2 | semidirect |
| 5. #22608122 | C2 | semidirect |
| 6. #22608120 | C2 | semidirect |
| 7. C73×#1420 | C2 | semidirect |
| 125. #1420 | D73 | semidirect |
| 128. C73 | #13625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989020 | 2 |
| M64×D73 | 2 |
| #368×D73 | 2 |
| #22608124 | 2 |
| #22608122 | 2 |
| #22608120 | 2 |
| C73×#1420 | 2 |
| #13625 | 73 |