Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #22608130 | C2 | semidirect |
| 3. C4⋊#14556497 | C2 | semidirect |
| 5. C73×#2252 | C2 | semidirect |
| 18. D1168 | Q8 | semidirect |
| 71. #2252 | D73 | semidirect |
| 76. C73 | #13703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1168 | 2 |
| #22608130 | 2 |
| C4⋊#14556497 | 2 |
| #22608108 | 2 |
| C73×#2252 | 2 |
| #13703 | 73 |