Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 196 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. #22624842 | C2 | semidirect |
| 17. #14556664 | C8 | semidirect |
| 25. C16×D73 | C8 | semidirect |
| 33. #11924031 | C2×C8 | semidirect |
| 42. #11924003 | C2×C8 | semidirect |
| 46. C16×C73 | C2×C8 | semidirect |
| 71. D73 | #1311 | semidirect |
| 76. C73 | C2×#1311 | semidirect |
| 118. C16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556664 | 2 |
| C8×#11924036 | 2 |
| #22624842 | 2 |
| C4×C16×D73 | 2 |
| C2×#1311 | 73 |