Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. D137⋊#108 | C2 | semidirect |
| 2. C2×#17984157 | C2 | semidirect |
| 4. #22578282 | C2 | semidirect |
| 16. #17984096 | C4 | semidirect |
| 17. #17984095 | C4 | semidirect |
| 19. #17984094 | C4 | semidirect |
| 24. #131×C137 | C4 | semidirect |
| 115. C137 | #1816 | semidirect |
| 128. #131 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| C2×#17984157 | 2 |
| #22578394 | 2 |
| #22578282 | 2 |
| #131×D137 | 2 |
| #1816 | 137 |