Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
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×#89137 | C2 | semidirect |
| 2. #20296023 | C2 | semidirect |
| 3. C2×#16812764 | C2 | semidirect |
| 4. #20296007 | C2 | semidirect |
| 5. #20295909 | C2 | semidirect |
| 6. #20295898 | C2 | semidirect |
| 25. #16812730 | C4 | semidirect |
| 26. #16812727 | C4 | semidirect |
| 28. #16812724 | C4 | semidirect |
| 32. #137×C109 | C4 | semidirect |
| 61. C2×D436 | C2×C4 | semidirect |
| 73. #13182013 | C2×C4 | semidirect |
| 77. C2×Q8×C109 | C2×C4 | semidirect |
| 80. M16×C109 | C2×C4 | semidirect |
| 151. C109 | #1906 | semidirect |
| 163. #137 | #89137 | semidirect |
| 195. C2×Q8 | C2×#89137 | semidirect |
| 217. M16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#89137 | 2 |
| #20296023 | 2 |
| C2×#16812764 | 2 |
| #20296007 | 2 |
| #20295909 | 2 |
| #20295898 | 2 |
| #20295825 | 2 |
| #1906 | 109 |