Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
244 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 244 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. #22627147 | C2 | semidirect |
| 2. D4×#11924040 | C2 | semidirect |
| 3. #22626996 | C2 | semidirect |
| 4. D4⋊#11924040 | C2 | semidirect |
| 5. D4⋊#11924040 | C2 | semidirect |
| 6. #22626947 | C2 | semidirect |
| 49. #11924040 | D8 | semidirect |
| 76. D4×C73 | M32 | semidirect |
| 121. C73 | #12038 | semidirect |
| 190. D4 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627147 | 2 |
| D4×#11924040 | 2 |
| #22626996 | 2 |
| D4⋊#11924040 | 2 |
| #22626947 | 2 |
| D8×#10596833 | 2 |
| #12038 | 73 |