Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #22581433 | C2 | semidirect |
| 3. #22581066 | C2 | semidirect |
| 4. #22581061 | C2 | semidirect |
| 5. C4×#14555774 | C2 | semidirect |
| 6. C2×#17984774 | C2 | semidirect |
| 7. #22580955 | C2 | semidirect |
| 8. #405×C139 | C2 | semidirect |
| 10. #17984864 | C4 | semidirect |
| 30. #14555785 | C2×C4 | semidirect |
| 37. Dic556 | C2×C4 | semidirect |
| 38. #14555774 | C2×C4 | semidirect |
| 39. D1112 | C2×C4 | semidirect |
| 47. C2×C8×C139 | C2×C4 | semidirect |
| 90. C139 | #2952 | semidirect |
| 99. #405 | D139 | semidirect |
| 133. C2×C8 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| #22581433 | 2 |
| #22581066 | 2 |
| #22581061 | 2 |
| C4×#14555774 | 2 |
| C2×#17984774 | 2 |
| #22580955 | 2 |
| #405×C139 | 2 |
| #2952 | 139 |