Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22612188 | C2 | semidirect |
| 2. #22611971 | C2 | semidirect |
| 4. #22607980 | C2 | semidirect |
| 5. #22607895 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 7. D4×Q16×C73 | C2 | semidirect |
| 79. Q16×C73 | D8 | semidirect |
| 103. D4×C73 | SD32 | semidirect |
| 146. D4×Q16 | D73 | semidirect |
| 153. C73 | #12318 | semidirect |
| 218. Q16 | #11924013 | semidirect |
| 254. D4 | #14556534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612188 | 2 |
| #22611971 | 2 |
| #22609286 | 2 |
| #22607980 | 2 |
| #22607895 | 2 |
| D4⋊#11924003 | 2 |
| D4×Q16×C73 | 2 |
| #12318 | 73 |