Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. Q8×#11924003 | C2 | semidirect |
| 4. #22607994 | C2 | semidirect |
| 6. C16×#10596831 | C2 | semidirect |
| 7. C73×Q8⋊C16 | C2 | semidirect |
| 46. #11924015 | C16 | semidirect |
| 57. #11924003 | SD16 | semidirect |
| 70. Q8×C73 | C2×C16 | semidirect |
| 88. #10596831 | C2×C16 | semidirect |
| 110. Q8⋊C16 | D73 | semidirect |
| 113. C73 | C16×SD16 | semidirect |
| 176. Q8 | C16×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924003 | 2 |
| #22611750 | 2 |
| C8×#11924015 | 2 |
| #22607994 | 2 |
| #22607887 | 2 |
| C16×#10596831 | 2 |
| C73×Q8⋊C16 | 2 |
| C16×SD16 | 73 |