Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22611732 | C2 | semidirect |
| 3. #22608685 | C2 | semidirect |
| 4. #22607902 | C2 | semidirect |
| 5. #22607900 | C2 | semidirect |
| 6. #22607898 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 72. Dic292 | M16 | semidirect |
| 96. D8×C73 | M16 | semidirect |
| 163. #1333 | D73 | semidirect |
| 164. C73 | #11666 | semidirect |
| 234. D8 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556610 | 2 |
| #22611732 | 2 |
| #22608685 | 2 |
| #22607902 | 2 |
| #22607900 | 2 |
| #22607898 | 2 |
| C73×#1333 | 2 |
| #11666 | 73 |