Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#17984875 | C2 | semidirect |
| 3. C2×#17984842 | C2 | semidirect |
| 4. #22581347 | C2 | semidirect |
| 5. #22581333 | C2 | semidirect |
| 6. #22581326 | C2 | semidirect |
| 7. C4×M16×C139 | C2 | semidirect |
| 44. M16×C139 | D4 | semidirect |
| 75. C4×C139 | #137 | semidirect |
| 83. C139 | #3152 | semidirect |
| 91. C4×M16 | D139 | semidirect |
| 124. M16 | D556 | semidirect |
| 161. C4 | #17984875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| #22581503 | 2 |
| C2×#17984842 | 2 |
| #22581347 | 2 |
| #22581333 | 2 |
| #22581326 | 2 |
| C4×M16×C139 | 2 |
| #3152 | 139 |