Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22611734 | C2 | semidirect |
| 3. #22607900 | C2 | semidirect |
| 4. #22607897 | C2 | semidirect |
| 5. C73×#1566 | C2 | semidirect |
| 65. Dic292 | M16 | semidirect |
| 68. D584 | M16 | semidirect |
| 150. #1566 | D73 | semidirect |
| 153. C73 | #11666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556613 | 2 |
| #22611734 | 2 |
| #22607900 | 2 |
| #22607897 | 2 |
| C73×#1566 | 2 |
| #11666 | 73 |