Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22621402 | C2 | semidirect |
| 2. #22611882 | C2 | semidirect |
| 4. #22607918 | C2 | semidirect |
| 5. #22607915 | C2 | semidirect |
| 6. #22607884 | C2 | semidirect |
| 7. C73×#2053 | C2 | semidirect |
| 175. #2053 | D73 | semidirect |
| 179. C73 | #12172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621402 | 2 |
| #22611882 | 2 |
| #22611877 | 2 |
| #22607918 | 2 |
| #22607915 | 2 |
| #22607884 | 2 |
| C73×#2053 | 2 |
| #12172 | 73 |