Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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. #41×#10587739 | C2 | semidirect |
| 2. #22578400 | C2 | semidirect |
| 3. C2×#17984153 | C2 | semidirect |
| 4. #22578384 | C2 | semidirect |
| 5. #22578286 | C2 | semidirect |
| 6. #22578275 | C2 | semidirect |
| 25. #17984119 | C4 | semidirect |
| 26. #17984116 | C4 | semidirect |
| 28. #17984113 | C4 | semidirect |
| 32. #137×C137 | C4 | semidirect |
| 61. C2×D548 | C2×C4 | semidirect |
| 73. #14555494 | C2×C4 | semidirect |
| 77. C2×Q8×C137 | C2×C4 | semidirect |
| 80. M16×C137 | C2×C4 | semidirect |
| 150. C137 | #1906 | semidirect |
| 163. #137 | #10587739 | semidirect |
| 195. C2×Q8 | C2×#10587739 | semidirect |
| 217. M16 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10587739 | 2 |
| #22578400 | 2 |
| C2×#17984153 | 2 |
| #22578384 | 2 |
| #22578286 | 2 |
| #22578275 | 2 |
| #22578202 | 2 |
| #1906 | 137 |