Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 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×#17984864 | C2 | semidirect |
| 2. #22581503 | C2 | semidirect |
| 3. #22581337 | C2 | semidirect |
| 4. #22581333 | C2 | semidirect |
| 5. #22581330 | C2 | semidirect |
| 6. #22581326 | C2 | semidirect |
| 7. C2×C4×C8×C139 | C2 | semidirect |
| 36. C2×C8×C139 | D4 | semidirect |
| 65. C4×C139 | #135 | semidirect |
| 72. C139 | #3147 | semidirect |
| 80. C2×C4×C8 | D139 | semidirect |
| 107. C2×C8 | D556 | semidirect |
| 139. C4 | #17984864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| #22581503 | 2 |
| #22581337 | 2 |
| #22581333 | 2 |
| #22581330 | 2 |
| #22581326 | 2 |
| C2×C4×C8×C139 | 2 |
| #3147 | 139 |