Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
758 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24918378 | C2 | semidirect |
| 2. C2×#19128077 | C2 | semidirect |
| 3. #24908303 | C2 | semidirect |
| 4. #24906131 | C2 | semidirect |
| 5. #24905914 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#3151 | C2 | semidirect |
| 116. M16×C83 | D8 | semidirect |
| 204. #3151 | D83 | semidirect |
| 210. C83 | #10144 | semidirect |
| 315. M16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918378 | 2 |
| C2×#19128077 | 2 |
| #24908303 | 2 |
| #24906131 | 2 |
| #24905914 | 2 |
| #24905301 | 2 |
| C83×#3151 | 2 |
| #10144 | 83 |