Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22577533 | C2 | semidirect |
| 4. #22577156 | C2 | semidirect |
| 5. #22577135 | C2 | semidirect |
| 7. #322×C137 | C2 | semidirect |
| 60. C8×C137 | M16 | semidirect |
| 77. C137 | #1592 | semidirect |
| 85. #322 | D137 | semidirect |
| 138. C8 | #14555493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577533 | 2 |
| C4×#14555499 | 2 |
| #22577482 | 2 |
| #22577156 | 2 |
| #22577135 | 2 |
| #22577132 | 2 |
| #322×C137 | 2 |
| #1592 | 137 |