Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
453 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 453 conjugacy classes of subgroups — too many to draw. Only its 80 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. #13098718 | C2 | semidirect |
| 4. #13098677 | C2 | semidirect |
| 6. #13097886 | C2 | semidirect |
| 7. #13097848 | C2 | semidirect |
| 25. C25×#104 | C4 | semidirect |
| 26. #11716385 | C4 | semidirect |
| 27. #11716373 | C4 | semidirect |
| 28. #11716353 | C4 | semidirect |
| 60. M16×C25 | C2×C4 | semidirect |
| 61. C42×C25 | C2×C4 | semidirect |
| 63. C4×Dic25 | C2×C4 | semidirect |
| 64. #87716 | C2×C4 | semidirect |
| 83. Q8×C25 | C4⋊C4 | semidirect |
| 85. D4×C25 | C4⋊C4 | semidirect |
| 96. D100 | C4⋊C4 | semidirect |
| 107. Dic50 | C4⋊C4 | semidirect |
| 260. #104 | #1035 | semidirect |
| 263. C25 | #1859 | semidirect |
| 304. M16 | C2×#1035 | semidirect |
| 321. C42 | C2×#1035 | semidirect |
| 333. Q8 | C4⋊#1035 | semidirect |
| 340. D4 | C4⋊#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13099678 | 2 |
| #13098783 | 2 |
| #13098718 | 2 |
| #13098677 | 2 |
| #104×D25 | 2 |
| #13097886 | 2 |
| #13097848 | 2 |
| #10604003 | 5 |