Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22611524 | C2 | semidirect |
| 3. #334×D73 | C2 | semidirect |
| 4. #22607902 | C2 | semidirect |
| 5. #22607900 | C2 | semidirect |
| 6. #22607898 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 29. #14556610 | C8 | semidirect |
| 73. Dic292 | C2×C8 | semidirect |
| 97. D8×C73 | C2×C8 | semidirect |
| 164. #1333 | D73 | semidirect |
| 165. C73 | #11598 | semidirect |
| 236. D8 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556610 | 2 |
| #22611524 | 2 |
| #334×D73 | 2 |
| #22607902 | 2 |
| #22607900 | 2 |
| #22607898 | 2 |
| C73×#1333 | 2 |
| #11598 | 73 |