Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22607871 | C2 | semidirect |
| 4. #22607870 | C2 | semidirect |
| 5. C73×#1322 | C2 | semidirect |
| 59. C2×C4×D73 | C16 | semidirect |
| 102. C2×C4×C73 | C2×C16 | semidirect |
| 112. C2×Dic73 | C2×C16 | semidirect |
| 156. D73 | #1322 | direct (N × H) |
| 161. #1322 | D73 | direct (N × H) |
| 162. C73 | C2×#1322 | semidirect |
| 277. C2×C4 | C16×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C8×D73 | 2 |
| C22⋊C16×D73 | 2 |
| #22607871 | 2 |
| #22607870 | 2 |
| C73×#1322 | 2 |
| C2×#1322 | 73 |