Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626707 | C2 | semidirect |
| 2. D73⋊#361 | C2 | semidirect |
| 3. #22626246 | C2 | semidirect |
| 4. #22626092 | C2 | semidirect |
| 5. #22625001 | C2 | semidirect |
| 6. #22624980 | C2 | semidirect |
| 24. C2×#14556536 | C4 | semidirect |
| 25. C2×#14556535 | C4 | semidirect |
| 26. C2×#14556532 | C4 | semidirect |
| 28. C2×D16×C73 | C4 | semidirect |
| 194. C73 | #13036 | semidirect |
| 203. C2×D16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626707 | 2 |
| D73⋊#361 | 2 |
| #22626246 | 2 |
| #22626092 | 2 |
| #22625001 | 2 |
| #22624980 | 2 |
| C2×#17989021 | 2 |
| #13036 | 73 |