Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 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. C2×#17984870 | C2 | semidirect |
| 2. #22581520 | C2 | semidirect |
| 3. C2×#17984838 | C2 | semidirect |
| 4. C2×#17984768 | C2 | semidirect |
| 5. #22580959 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 7. C2×#100×C139 | C2 | semidirect |
| 34. C2×Dic278 | D4 | semidirect |
| 40. C2×D556 | D4 | semidirect |
| 41. C2×D556 | D4 | semidirect |
| 50. C4⋊Dic139 | D4 | semidirect |
| 55. C4×Dic139 | D4 | semidirect |
| 67. M16×C139 | D4 | semidirect |
| 138. C139 | #2002 | semidirect |
| 145. C2×#100 | D139 | semidirect |
| 200. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984870 | 2 |
| #22581520 | 2 |
| C2×#17984838 | 2 |
| C2×#17984768 | 2 |
| #22580959 | 2 |
| #22580714 | 2 |
| C2×#100×C139 | 2 |
| #2002 | 139 |