Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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. C16×D292 | C2 | semidirect |
| 2. #22609293 | C2 | semidirect |
| 4. #22608005 | C2 | semidirect |
| 5. #22607980 | C2 | semidirect |
| 6. #22607977 | C2 | semidirect |
| 7. C73×#2248 | C2 | semidirect |
| 73. C16×C73 | D8 | semidirect |
| 89. D292 | SD32 | semidirect |
| 118. #2248 | D73 | semidirect |
| 125. C73 | #12432 | semidirect |
| 191. C16 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D292 | 2 |
| #22609293 | 2 |
| #22609283 | 2 |
| #22608005 | 2 |
| #22607980 | 2 |
| #22607977 | 2 |
| C73×#2248 | 2 |
| #12432 | 73 |