Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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. #27164461 | C2 | semidirect |
| 3. #27164402 | C2 | semidirect |
| 4. #27164136 | C2 | semidirect |
| 5. #27163835 | C2 | semidirect |
| 6. #27163832 | C2 | semidirect |
| 7. #364×C199 | C2 | semidirect |
| 74. C199 | #2212 | semidirect |
| 80. #364 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164461 | 2 |
| #27164456 | 2 |
| #27164402 | 2 |
| #27164136 | 2 |
| #27163835 | 2 |
| #27163832 | 2 |
| #364×C199 | 2 |
| #2212 | 199 |