Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22581751 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. #22581517 | C2 | semidirect |
| 4. #22580957 | C2 | semidirect |
| 5. #22580926 | C2 | semidirect |
| 6. #22580725 | C2 | semidirect |
| 7. #421×C139 | C2 | semidirect |
| 36. C2×Dic278 | D4 | semidirect |
| 43. C2×D556 | D4 | semidirect |
| 55. C2×C139⋊C8 | D4 | semidirect |
| 70. M16×C139 | D4 | semidirect |
| 142. C139 | #2008 | semidirect |
| 147. #421 | D139 | semidirect |
| 208. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581751 | 2 |
| C2×#17984870 | 2 |
| #22581517 | 2 |
| #22580957 | 2 |
| #22580926 | 2 |
| #22580725 | 2 |
| #421×C139 | 2 |
| #2008 | 139 |