Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
244 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611764 | C2 | semidirect |
| 3. #22608000 | C2 | semidirect |
| 4. D4⋊#11924003 | C2 | semidirect |
| 5. #22607885 | C2 | semidirect |
| 6. #22607847 | C2 | semidirect |
| 7. D4×C16×C73 | C2 | semidirect |
| 70. C16×C73 | D8 | semidirect |
| 74. D4×C73 | M32 | semidirect |
| 115. D4×C16 | D73 | semidirect |
| 121. C73 | #12038 | semidirect |
| 184. C16 | #11924013 | semidirect |
| 190. D4 | #14556530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611764 | 2 |
| C8×#11924013 | 2 |
| #22608000 | 2 |
| D4⋊#11924003 | 2 |
| #22607885 | 2 |
| #22607847 | 2 |
| D4×C16×C73 | 2 |
| #12038 | 73 |