Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #20295433 | C2 | semidirect |
| 4. #20295431 | C2 | semidirect |
| 5. #20295429 | C2 | semidirect |
| 6. #20295422 | C2 | semidirect |
| 9. #498×C109 | C2 | semidirect |
| 43. #13182012 | Q8 | semidirect |
| 86. C8×C109 | C2×Q8 | semidirect |
| 87. #11724784 | C2×Q8 | semidirect |
| 107. C109 | #3165 | semidirect |
| 114. #498 | D109 | semidirect |
| 194. C8 | Q8×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295581 | 2 |
| C4⋊Q8×D109 | 2 |
| #20295433 | 2 |
| #20295431 | 2 |
| #20295429 | 2 |
| #20295422 | 2 |
| #20295065 | 2 |
| C4×#13182012 | 2 |
| #498×C109 | 2 |
| #3165 | 109 |