Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#13182014 | C2 | semidirect |
| 2. C2×#16812673 | C2 | semidirect |
| 3. C2×#16812620 | C2 | semidirect |
| 4. C2×#16812619 | C2 | semidirect |
| 5. C2×C22⋊#11724784 | C2 | semidirect |
| 6. #20294788 | C2 | semidirect |
| 7. C2×#121×C109 | C2 | semidirect |
| 35. C2×D436 | D4 | semidirect |
| 46. C2×#11724784 | D4 | semidirect |
| 48. C4⋊Dic109 | D4 | semidirect |
| 60. C2×D4×C109 | D4 | semidirect |
| 71. C4⋊C4×C109 | D4 | semidirect |
| 86. C23×C109 | D8 | semidirect |
| 172. C109 | #1999 | semidirect |
| 175. C2×#121 | D109 | semidirect |
| 221. C2×D4 | C22⋊D109 | semidirect |
| 242. C4⋊C4 | C22⋊D109 | semidirect |
| 265. C23 | #13182014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182014 | 2 |
| C2×#16812673 | 2 |
| C2×#16812620 | 2 |
| C2×#16812619 | 2 |
| C2×C22⋊#11724784 | 2 |
| #20294788 | 2 |
| C2×#121×C109 | 2 |
| #1999 | 109 |