Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×D2336 | C2 | semidirect |
| 2. C2×#17988422 | C2 | semidirect |
| 3. #22612179 | C2 | semidirect |
| 4. C32×Dic73 | C2 | semidirect |
| 5. C2×D32×C73 | C2 | semidirect |
| 24. #14556497 | D4 | semidirect |
| 29. C32×C73 | D4 | semidirect |
| 63. Dic73 | D32 | semidirect |
| 71. C2×D32 | D73 | semidirect |
| 74. C73 | #13725 | semidirect |
| 98. C32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2336 | 2 |
| C2×#17988422 | 2 |
| #22612179 | 2 |
| C32×Dic73 | 2 |
| C2×D32×C73 | 2 |
| #13725 | 73 |