Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22581753 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. #22581522 | C2 | semidirect |
| 4. #22580969 | C2 | semidirect |
| 5. #22580959 | C2 | semidirect |
| 6. #22580926 | C2 | semidirect |
| 7. #344×C139 | C2 | semidirect |
| 41. C2×Dic278 | D4 | semidirect |
| 50. C2×D556 | D4 | semidirect |
| 69. M16×C139 | D4 | semidirect |
| 71. C2×C8×C139 | D4 | semidirect |
| 142. C139 | #2008 | semidirect |
| 150. #344 | D139 | semidirect |
| 208. M16 | D556 | semidirect |
| 210. C2×C8 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| C2×#17984870 | 2 |
| #22581522 | 2 |
| #22580969 | 2 |
| #22580959 | 2 |
| #22580926 | 2 |
| #344×C139 | 2 |
| #2008 | 139 |