Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×Dic398 | C2 | semidirect |
| 2. #27164364 | C2 | semidirect |
| 3. #27164215 | C2 | semidirect |
| 4. #27163763 | C2 | semidirect |
| 5. #27163748 | C2 | semidirect |
| 6. D4⋊(C199⋊C8) | C2 | semidirect |
| 55. Dic398 | D8 | semidirect |
| 70. D4×C199 | SD16 | semidirect |
| 99. C199 | #1627 | semidirect |
| 164. D4 | #15691874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic398 | 2 |
| #27164364 | 2 |
| #27164215 | 2 |
| #27163763 | 2 |
| #27163748 | 2 |
| D4⋊(C199⋊C8) | 2 |
| #459×C199 | 2 |
| #1627 | 199 |