Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
538 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 113 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. (C2×#10596842)⋊Q8 | C2 | semidirect |
| 3. C2×#17989677 | C2 | semidirect |
| 4. C2×Q8⋊#10596842 | C2 | semidirect |
| 6. C2×#17989671 | C2 | semidirect |
| 63. C2×#11924017 | C8 | semidirect |
| 64. C2×#11924016 | C8 | semidirect |
| 65. C2×#11924015 | C8 | semidirect |
| 69. C2×SD16×C73 | C8 | semidirect |
| 177. C8×C73 | C22⋊C8 | semidirect |
| 178. #10596831 | C22⋊C8 | semidirect |
| 219. C73 | #9660 | semidirect |
| 247. C2×SD16 | #10596842 | semidirect |
| 390. C8 | C22⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10596842)⋊Q8 | 2 |
| #22627081 | 2 |
| C2×#17989677 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C2×D4⋊#10596842 | 2 |
| C2×#17989671 | 2 |
| C2×SD16×#64408 | 2 |
| #9660 | 73 |