Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924040 | C2 | semidirect |
| 3. #22626989 | C2 | semidirect |
| 4. Q8⋊#11924040 | C2 | semidirect |
| 6. #22626947 | C2 | semidirect |
| 48. #11924040 | SD16 | semidirect |
| 70. Q8×C73 | M32 | semidirect |
| 113. C73 | #12050 | semidirect |
| 176. Q8 | #14556688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| #22627146 | 2 |
| #22626989 | 2 |
| Q8⋊#11924040 | 2 |
| #22626974 | 2 |
| #22626947 | 2 |
| #22625515 | 2 |
| #12050 | 73 |