Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
122 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 46 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×#17984573 | C2 | semidirect |
| 2. C2×#17984572 | C2 | semidirect |
| 3. #22579947 | C2 | semidirect |
| 4. #22579937 | C2 | semidirect |
| 5. C22⋊#14555667 | C2 | semidirect |
| 6. C4×#14555667 | C2 | semidirect |
| 24. #14555667 | D4 | semidirect |
| 47. Dic277 | M16 | semidirect |
| 55. C277 | #436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984573 | 2 |
| C2×#17984572 | 2 |
| #22579947 | 2 |
| #22579937 | 2 |
| C22⋊#14555667 | 2 |
| C4×#14555667 | 2 |
| #22579840 | 2 |
| #436 | 277 |