Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22612159 | C2 | semidirect |
| 3. #22609549 | C2 | semidirect |
| 5. C73×#1312 | C2 | semidirect |
| 64. C8×C73 | SD32 | semidirect |
| 84. #1312 | D73 | semidirect |
| 85. C73 | #12526 | semidirect |
| 144. C8 | #14556536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612187 | 2 |
| #22612159 | 2 |
| #22609549 | 2 |
| #22609523 | 2 |
| C73×#1312 | 2 |
| #12526 | 73 |