Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. #22620922 | C2 | semidirect |
| 2. #22620023 | C2 | semidirect |
| 3. #22619927 | C2 | semidirect |
| 4. #22608399 | C2 | semidirect |
| 5. #22608271 | C2 | semidirect |
| 6. #22607792 | C2 | semidirect |
| 7. C73×#1536 | C2 | semidirect |
| 210. #1536 | D73 | semidirect |
| 214. C73 | #10038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620922 | 2 |
| #22620023 | 2 |
| #22619927 | 2 |
| #22608399 | 2 |
| #22608271 | 2 |
| #22607792 | 2 |
| C73×#1536 | 2 |
| #10038 | 73 |