Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
362 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #22624892 | C2 | semidirect |
| 4. #22624891 | C2 | semidirect |
| 69. Dic292 | M16 | semidirect |
| 89. Q16×C73 | M16 | semidirect |
| 149. C73 | #11664 | semidirect |
| 214. Q16 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626295 | 2 |
| #22625486 | 2 |
| #22624892 | 2 |
| #22624891 | 2 |
| C4×Q16×D73 | 2 |
| #11664 | 73 |