Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #19136392 | C2 | semidirect |
| 3. #19133352 | C2 | semidirect |
| 4. #19132559 | C2 | semidirect |
| 5. #19132557 | C2 | semidirect |
| 6. #19132555 | C2 | semidirect |
| 7. C43×#1332 | C2 | semidirect |
| 74. Q16×C43 | M16 | semidirect |
| 97. D344 | M16 | semidirect |
| 159. #1332 | D43 | semidirect |
| 186. C43 | #11660 | semidirect |
| 234. Q16 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13063348 | 2 |
| #19136392 | 2 |
| #19133352 | 2 |
| #19132559 | 2 |
| #19132557 | 2 |
| #19132555 | 2 |
| C43×#1332 | 2 |
| #11660 | 43 |