Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16837837 | C2 | semidirect |
| 2. #21433812 | C2 | semidirect |
| 3. #21433745 | C2 | semidirect |
| 4. C2×#16837216 | C2 | semidirect |
| 5. #21425723 | C2 | semidirect |
| 6. #21422212 | C2 | semidirect |
| 7. C59×#2145 | C2 | semidirect |
| 59. #14273667 | D4 | semidirect |
| 62. #14273663 | D4 | semidirect |
| 71. C2×Q16×C59 | D4 | semidirect |
| 73. C2×D8×C59 | D4 | semidirect |
| 209. #2145 | D59 | semidirect |
| 242. C59 | #13310 | semidirect |
| 255. C2×Q16 | D236 | semidirect |
| 263. C2×D8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| #21433812 | 2 |
| #21433745 | 2 |
| C2×#16837216 | 2 |
| #21425723 | 2 |
| #21422212 | 2 |
| C59×#2145 | 2 |
| #13310 | 59 |